Well, the animal will only have the same DNA as the old one; won't be an exact copy, but I think (hope) most everyone here already knew that.
But obviously, a majority of people who would waste their money on this either believe or are simply deluded enough to believe that it will be the exact same pet. A grieving pet-owner isn't going to let a little thing like scientific truth get in the way of getting their beloved Mr. Fluffers back.
Ever see "the Sixth Day"?
Anyway, I do think that cloning might be the only way to bring endangered species like salmon from the edge of extinction and bring dinosaurs back to life.
Cloning is not a viable way of restoring an endangered or extinct species, nor should modern cloning ever be used on humans. Here's why.
The cloning process does not use embryonic DNA. It uses adult DNA. Adult DNA in all organisms exhibits modified gene expression from that of the embryo. We can fool it into acting like an mebryonic cell, but the expression pattern never totally reverses - some genes are totally modified in adulthood and they cannot be restored to their original form from an embryo.
The result is the major health problems which we see in most cloned animals; notably, behavioural discrepancies, weight gain and obseity, and early organ failure. This is why cloning is NOT used to maintain labratory strains of specific genotypes in a species under study.
As for "bringing the dinosaurs back," the DNA half-life is incredibly short; the only DNA from Neanderthal remains that is usable in any kind of study is from mitochondria. Cellular DNA is pretty much degraded beyond repair. Considering that dinosaurs roamed the Earth some 300 million years ago, it's not going to be recovered, even encased in amber =)
Frankly, I think it is totally irresponsible for anyone to be cloning anything if they are not a licensed researcher affiliated with a private lab or university with full ethical grounds in place.
At any rate, cloning is a science that is extremely misunderstood, largely thanks to mass media that doesn't have an effing clue.