Long version: assuming this NYT article isn't just the wearyingly familiar contraction of scientific progress (it's strange how "We can't entirely rule out that one day we might be able to X" always seems to morph into "Top scientists now say they can X tomorrow!!!1!"), the idea of getting close to being able to clone species extinct for up to 60,000 years brings mixed feelings.
Obviously, the idea of humanity actually being responsible for increasing the bio-diversity of the planet is quite an attractive one. Not only could we bring back some of the species we are directly or indirectly pushed out of existence (I feel particularly bad about the passenger pigeon, if anyone has some spare DNA from those lying around), but we could bring back stuff that got screwed for totally different reasons. I know that on any rational level that makes no sense, but my inner tree-hugger quite likes the idea of there being at least one species that's back because of us.
On the other hand, if we do decide to grow ourselves some new tarpans or indefatigable Galapagos mice (apparently not so indefatigable as claimed), what the hell do we do with them? We have enough trouble fiddling around with the populations of the animals we have now. Any species that went extinct without our interference did so for some reason or other, we can't just stick them back in the same place they came from and hope this time they get their shit together. Plus, a lot of the damage we've caused was from messing up habitats (it's no coincidence so many entries in Wikipedia's list of extinct mammals are creatures that lived on islands), which again raises the question of what we're going to do with our brand new giant tree rat. Maybe there's an animal here or there that we just brutally, directly fucked, by hunting the crap out of it or something, and we might be able to reinsert them into the wild without knocking over a huge chain of dominoes.
Otherwise, we'd just be talking about bringing these creatures into captivity, and beginning breeding programmes. Which, in fairness, is something we're already doing with a number of species that are now extinct in the wild, but the fact that such wild extinctions have been relatively recent and that the creatures are still alive and kicking makes it easier to justify releasing them if and when we have enough to make it worth trying.
I'm not sure where I stand on the morality of bringing back extinct species just so that we can point to them in zoos. Breeding programmes to keep species alive is one thing, but maybe we shouldn't be considering the hi-tech cloning equivalent of grave-robbing.
Short version: I want to see a quagga fight a thylacine and none of you motherfuckers are going to stop me!