Well, this is right up my alley, isn't it?
It turns out that, no matter how well-preserved something's body is, DNA still degrades over time. Unless the unique conditions allow the DNA to be preserved as well, even the best-preserved mammoths in ice will have no intact DNA left. Unfortunately, DNA is best preserved in acidic environments (since DNA is, itself, an acid), which have a tendency not to preserve the body of the animal. There are a few exceptions, though. There have been fossils found in peat layers that used to be acidic bogs, so there's some promise for extracting well-preserved DNA.
However, even degraded DNA is not completely useless. If enough different strands are patched together (and no, I am not talking about using frog DNA, I'm talking about using many different samples of the degraded DNA of the animal you're trying to create), matching segments can be lined up, and the entire DNA sequence could theoretically be determined. But nobody has yet attempted such a daunting undertaking, and it would probably take years, if not decades, to complete.
And as much as I hate to admit it, but, barring time travel, obtaining the DNA of dinosaurs is probably out of the question. They
have actually obtained DNA from insects in amber (an insect from the time of the dinosaurs, even), but they couldn't find enough intact DNA to even re-create the insect, let alone a dinosaur. And, although soft tissue and actual cells have been found inside dinosaur bone, no DNA has ever been found.
EDIT: I did a little more research, and it turns out that some
claim to have found dinosaur DNA, but in every case, the results have not been able to be replicated by other scientists, so it's a little sketchy whether they actually did or not.