There's quite a few drawbacks technologically that makes this a difficult proposition. I listed them in the other thread, but here they are again (don't worry, its a good idea to make this thread, I'm just getting people caught up to the discussion):
1. Cloning involves taking adult DNA and forcing it to act like the DNA of an embryo. The problem is that adult DNA has been degraded by time, and the resulting clone will have the DNA of an adult specimen. Unless we can clone from embryos, that means that the clone will have a host of physical problems from an early age.
2. Current cloning techniques require a viable egg cell. In some cases we think we can get away with using a different, but similar, species egg cells, but it may be that there simply is not a living species that can offer a host egg with the proper chemistry to work with an extinct animals' DNA. For mammals you also need a womb that the cloned embryo can survive in, and if the species is gone it might not be that easy to find such a thing. Also, we know nothing about the hormones that an extinct animal needs to develop properly, so it could turn out that we can only get female clones, or parts of the embryo are simply missing, or any number of developmental disorders could arise.
3. A lot of extinct species only offer up broken strands of DNA. We'd have to make some guesses when repairing these strands, and possibly fill in some blanks ourselves. That means that ultimately, we aren't creating the species, but a similar organism with similar features. Can you really call it a wooly mammoth if you had to fill in some DNA with african elephant DNA?
4. Somebody wants to clone the neanderthal. That should not be allowed - the guys were just as smart as us, but physically much stronger. They simply died out due to climate change making their preferred hunting habits (sneaking up an animals then stabbing them and beating them with weapons at melee range) impossible. Do we really want to bring back our possible replacement? And what about neanderthal rights - are they people, or do they belong in a zoo?
5. There are better options for animals that are highly endangered. Zoos could freeze embryos from critically endangered species, then turn them over to wildlife groups working to reintroduce species to the wild. The problem is zoos don't really have an economic incentive to do this, so it doesn't happen all that often. There have been a few exceptions, though, like the European Bison mentioned earlier, and the california condor, but the general rule is zoos should not be relied upon when it comes to protecting a species (a better model would be the panda reserves China has set up, which do have as their goal reintroduction to the wild and are funded by the government so they aren't motivated by economics alone).
All that being said, some species ought to be brought back if they can be, because without them their ecosystems are collapsing. The problem is that before we try such programs, we have to make sure that the things which wiped the species out in the first place are fixed. For example, dodo birds were driven extinct by the introduction of pigs and rats to Mauritus, so before we can bring back the dodo to the island we have to kill off every last rat and pig on the island - probably an impossible task. So dodos are likely going to remain dead as a dodo in the wild, even if we do bring them back through cloning. The thylacine, on the other hand, might do just fine, so long as Tasmanian shepherds don't shoot the things. Of course, reintroducing the thylacine could have consequences for the tasmanian devil, which is on the ropes itself due to a plague and probably couldn't do with the competition with another predator at the moment. Thing is, it might actually help the devil too, since the theory goes that the tasmanian devils ate what was left over by the thylacines. Reintroduction has to be handled in a very careful and controlled manner, really.