Dinosaurs were/are a very special group of reptiles that have some notably different attributes than most other groups of reptiles and are believed by many to have gone extinct roughly 65 million years ago. Many were very large, such a Sauropods (long necked) dinosaurs, some of which may have grown to nearly 200 feet long and weighed over 100 tons. Other dinosaurs were as small as a common chicken and ran about on two hind legs hunting prey.
   Many people teach and believe that dinosaurs reigned on our planet from about 230-65 million years ago and were then wiped out by some unknown force (the most popular theory is an asteroid struck the Gulf of Mexico) and were wiped from our planet along with numerous other organisms and thus never lived within several tens of millions of years of humans due to evolutionary timelines.

   Many people call Pterosaurs and Plesiosaurs/Pliosaurs Dinosaurs, technically they are NOT Dinosaurs since Dinosaurs according to classification refer only to the land dwelling creatures and not the flying or swimming ones that had different anatomy. Dinosaurs hadlegs that did not stick out to the sides like lizards and crocodilians, but instead were positioned mostly near/under the body in a much more erect manner.
Although for all intensive purposes one can group them together for purposes of discussion. But remember Pterosaurs, commonly called "Pterodactyls" and the marine reptiles like Plesiosaurs and the stockier, short necked Pliosaurs are not Dinosaurs.

However there are many that believe in contrast to the previous, that dinosaurs and man have cohabitated on the planet, if not since the beggining of Earth's history.

  The answer seems to depend on personal beliefs as well as science. We know that many dinosaurs have died at some point in the Earths' history because we have many millions of fossils that show it.

  If you believe that the world and nature are the results of Darwinian Evolution then you believe that dinosaurs went extinct about 65 million years ago, the point in the fossil record where Dinosaur fossils don't reach beyond is called the KT boundary.  Or that they evolved into birds (this belief is losing popularity among scientists due to lack of evidence*).

  If you believe in the account of Genesis from the Bible as a literal history of origins, then you believe that Dinosaurs and other "Prehistoric" animals were created during Creation week along with all the other kinds of life on our planet. They would have been created on the day according the thier environment as well, such as aquatic reptiles and flying reptiles created alongside the fish and the birds and the land dinosaurs created alongside the other land animals and man himself on the sixth day*.

  According to Biblical history (real history), Dinosaurs got on the ark and off it with all the other animals that boarded. After getting off the ark, the planet was much less habitable and animals and people would have a much harder time surviving. During the years to come, possibly a few centuries after the Flood, animals and man would have competed fiercely for food and space since both were in short supply.
  During these times people would have killed off any large or otherwise threatening animals to make life easier. Think about it, people still kill "chicken snakes" for eating their chicken eggs even though you can simply pick them up and set them in the woods. Obiously people would kill off any giant, 7 ton man or cattle eating reptiles and certainly develop stories and legends about such encounters.

*Some believe in the bible yet try to reconcile creation week with evolution. This causes a muddy mess because the two theories are like night and day and one will eventually run into a wall that cannot be surmounted. In addition, the account in Genesis specifically states that each day is a 24 hour period bordered by morning and evening, this should close the debate over the interpretation of time in "days" in Genesis.

Quite possibly.

There are many remote areas of the world in which native people have been reporting creatures that resemble nothing other than certain species of dinosaurs since outsiders first made contact with them. They say that they have known about the creatures for far longer than they have known of outsiders and have not heard of the teachings of "modern" man so they do not understand that these creatures are supossed to be extinct.

The field of Cryptozoology is a field that searches for and studies unclassified animals and there are several organizations looking for living dinosaurs. The animals that natives report have local names, not the names outsiders know them as. Not all natives actually believe these mysterious creatures to be real animals, instead they believe them to be legends or even gods, yet does this fact discredit that the creatures reported are actual physical animals? Some may say so, but upon closer inspection it is not that simple. The line of reasoning that if not every single person believes a local legendary creature to be a physical animal seems to imply that majority rules.

   Yet it only goes to reason that some people from an area will not believe in a creature if they have not seen it and it is not well known. However the majority of locals that have been questioned about creatures that have been reported to resemble a dinosaur, have expressed a firm belief that the animals they are questioned about are real animals such as any other in their local fauna like an elephant or lion or crocodile, and not merely a legend or deity.

Reasoning follows that many of the natives of areas that do not believe these mystery animals to be real are the people who have not seen them themselves, this type of dismissal is evident in all cultures. Many Americans claim to have seen animals that seem to be dinosaurs while many others say they are either crazy, mistaken, or that their sighting was the result of drug induced hallucinations or alcohol since they themselves have not seen such creatures.

If these creatures are real as the local people claim, it seems that if more locals believe them real than mythical, these reported, albeit rare, animals may in fact be living, breathing creatures and not just local legends, and may in fact represent small, relicit populations of surviving speies of Dinosaurs, Pterosaurs or marine reptiles.

  Well, first off, there are relatively very few people searching for these animals. The environments in which the creatures are reported are places that are poorly and in some places not explored at all by outsiders. The places are harsh, unforgiving terrain in many cases, such as the African Congo which is a jungle/swamp almost the size of Florida, USA with numerous dangers.
 Many of the dangers include civil war, unhospitable locals, crocodiles, venomous snakes, quicksand, large dangerous non predatory animals, predatory wildlife, giant pythons and boas that lay in ambush, drowning, parasites, disease and Mosquitoes which kill more people than any other animal.

In addition to the dangers, the few people that are looking for these creatures are on self funded expeditions so they have very limited funds, time and equipment, this also means that any lost or damaged equipment is hard to replace.
  Also, it is very hard to get a good picture of a wary animal, even an expensive camera may not be able to get a good enough shot, and many cases require a telescopic lens that can zoom in from very far away, these must be purchased and installed extra of the standard camera. Again, a wary animal is hard to photograph because it will disappear in about 1-10 seconds if it feels threatend, it takes several seconds at the minimum just to turn a camera on, find the animal with the camera, focus and snap a picture, this is assuming that the camera will focus based on the zoom and lighting.

  Even finding one of these creatures does not gauruntee that it will be filmed or photographed because sightings are many times too far off to capture adeqautely on film or get a picture of. And many encounters (especially up close ones) last only a few seconds, longer than most cameras take to even start up let alone take a good and balanced, clear photograph.

  These are very likely not just tall tales because there is some evidence in the form of video, photographs and physical evidence such as footprints, dens, feeding areas, and other evidence. In addition, the vast majority of eye witnesses report the same description of the creatures they see, but in any case some small degree of incosistancy is inevitable such as some size disecrepancies and color differences.
  The reports come from many different people from many different cultures around the world yet all seem to sync up to a known arhcetype (body plan, eg. a long necked Sauropod Dinosaur) of animal that vary from one location in the world to another.

  Yes. there is much evidence of just that. There are many artifacts and pieces of art, as well as stories that depict creatures that look very similar to dinosaurs. Many of them so clearly that there should be no question as to the creature in question.

  Some depictions however have been depicted with "artistic license" but it remains clear what animal is depicted. Aside from these,there are plenty of legends and stories of giant reptiles, some are even from modern times.

Yes Dragons. Many dragons depicted throughout history strongly resemble certain species of dinosaurs. The stereotypical giant, four legged, winged, fire breathing dragons that most are familiar with are a relatively recent interpretation but they do have basis in reality.

Winged dragons for example were only depicted with two legs until only a few hundred years ago. They are also depicted with some sort of ornamentation on the back of their head, having a long tail with an ornament on the tip, batlike wings and are reptilian.

Four legged dragons were in turn, not depicted with wings and may have been described differently depending on the place they were from. Some stories even specifically describe bipedal, or two legged dragons.

Many resembled different species of dinosaurs such as sauropods, ceratopsians (triceratops, etc.), Baryonyx, Tyrannosaurus, Stegosaurus, and several others. Dragons were always regarded as real animals and were included in Bestiaries, catalogoues of wildlife and were shown in art alongside well known animals like monkeys, bulls, deer, fish and lions.

It is not as far fetched as many think for an animal to breathe fire. There are animals that use other complex defense systems such as the Bombardier beetle which uses rocket full to blast enemies with a burst a super ot chemicals as hot as fire. And there is the Electric Eel that uses electricity to shock potential enemies or predators. It would not be out of the question for an animal to produce and combine chemicals and expel them causing them to ignite in the oxygen filled atmosphere. This certainyl sounds crazy to many but in the context of animal defense mechanisms it actually is quite possible. So to say that a Dinosaur couldn't breathe fire is far from reality.

While it cannot be proven, there are many stories and even depictions of dinosaurs breathing fire. There is even a recent yet little known story from Niger, Africa of a small spinosaurus being encountered by a desert village that reports it could breathe fire. This story seems true but has not been fully confirmed. It is not fully certain the mechanism these creatures used to project fire but many dinosaurs have cavaties in their skulls that scientists do not know the function of. Skeptics say that there is no evidence from the fossil record that these animals could "breathe fire" but the fossil record cannot tell us about the mechamisms and internal actions of a living creature or the chemistry it would use to produce something like fire, ie. the fossil record cannot tell us that a firefly can produce a glow or that a bombardier beetle could use rocket fuel to produce an explosion out of its abdomen.

That is a good question. The theory of evolution states that dinosaurs should not be alive today  because they have either gone extinct or evolved into birds and that they are not found in sediment layers more recent than 65 million years old. Finding a dinosaur species* still living today as a set species would show that Evolutionary geology, dating and biological theories are in serious need of correction** since it has long been taught by evolutionary proponents that Darwinian evolution is the only explanation for life and that it is backed up by observation and facts.

If dinosaurs, one of evolutions biggest star examples of proof, turn out to be no proof at all, then why not take a second look at the rest of its examples? In reality, finding a living dinosaur would not change the thoughts on and philosophies on origins and scientific processes to many that hold the Humanist view, but it would certainly sway some. Also, if evolution were true, 65 million years is a long time for a species to remain unchanged. The 6000 years that is understood from a literal reading of Genesis would make it much easier for a species of dinosaur to remain alive and a few hundred is not very long for a small population to remain undetected to "modern man".

*in order for one to be alive, a population of the species would have to be alive and able to come together and breed. There is a decent amount of evidence that most dinosaurs living together do have migration routes.

**Evolution theories say that there is indisputable proof of their claims and that the fossil record is a perfect example the history of an old Earth with many transitional forms.

  Not really, no. In fact there are no fossils that are accepted as indisputable proof of one kind of organism turning into another, there have been many fossils said to be "missing links" but they have all been proven false, retracted after more examination took place, or dissapeared.

  Many are made up from bones of different creatures or even illustrations made of a creature from just one single bone or tooth, yet all missing links have been prematurely declared proof only to be later revealed to be something that is a set species and kind or even hoaxes that were made up by proponents of Evolution to provide proof or created by individuals that sought to make money.

  In reality there have been no fossils found that clearly show one organism changing to another. All fossils known show stable creatures that are not changing into or from anything else. In fact, virtually every organism alive today is the same as it was in the fossil record, again showing stability of species throughout history. The opposite of Macro-Evolutionary claims and predictions.

  The fossils of dinosaurs bearing feathers is a subject of continued debate. The idea has recently been rejected by a group of scientists saying that the feathers are in fact collagen fibers, which makes much more sense upon examination of the fossils. Most of the "feathers" are little more than fibrous strands of tissue along the outer edges of the fossil or in some cases just simple lines that radiate from the skeleton.

  These "proto feathers" as they have been dubbed have been compared to the fossilized remains of other animals that are known to have never had feathers, such as sharks, and were found to match perfectly with the splayed collagen fibers exhibited by those animals. Many researchers have commented as saying that the collagen fibers are likely the remains of what used to be a frill running along the animals body, the collagen fibers would have been a key structural support feature to such an anatomical asset and points to reptile anatomy than bird anatomy.

As of yet there have been no fossils of any type of dinosaurs that exhibit clear and obvious feathers. And even though they are presented as established fact, there is in reality no true consensus on the matter and the evidence is underwhelming at best, if not, in reality, completely lacking. However the idea has become so popular and ingrained to some that many Theropod dinosaur species have been portrayed with feathers even if no evidence of "proto feathers" has been found on the species.

In addition, scientists cannot seem to agree on how dinosaurs started to evolve into birds, let alone explain the severe barriers of transforming a reptile into a bird. In fact, many now believe that  many aspects of the supposed evolution of birds went the opposite direction as previously thought. The topic is discussed in more detail in the section on Dnosaurs on our site. Scales to Feathers