I would bring back Castoroides ohioensis. I’ve always been partial to furry little beavers, but I find the thought of coming (sp?) upon a giant beaver quite intriguing.
*Homo neandertalensis *would be the most intriguing, not only to see if they could hybridize with us (I’d volunteeer:)), but especially to hear their language.
Assuming neanderthals had language ability (I do not know) language is a learned trait. We are not born knowing English or Spanish. We are taught it.
As such I suspect neanderthals would speak English (or the language of whatever researcher brought them back).
The missing link.
Which one…?
Ah, that’s easy, one of the extinct species of giant tortoise (or, hell, more of the existing animals). The Wikipedia page contains this gem,
While Wikipedia can be flaky, I learned about them from an episode of QI (transcript):
Yeah, silphium was cool at the time, but we have more reliable contraceptives now. If you had animals that tasty you could sell them at any cost, even after factoring in the cost of cloning and the slow growth rate. Velocirators? No way, ICBMs would be cheaper and more effective.
Well, really, nothing had a scientific name (at least, not as we know them) until a good 200 years after the Galapagos Islands (and thus, the tortoises) were discovered. So they were only absent a unique name between 1735 (when Linnaeus published his Systema Naturae) and 1827 (when Harlin published a description of the “elephant tortoise”, giving it the name of Testudo (now Geochelone) elephantopus).
I knew I was tempting fate to post that directly after you, but couldn’t resist.
Seriously though, that’s an interesting point. It does rather diminish the romance of the story, but there’s plenty left what with them being used as living food and water stores on ships. Ah, we’re capable of such limitless cruelty.
The one that made the connection earliest.
Which connection? The most recently extinct common ancestor of Homo Sapiens and its nearest living relative (Tough to pin down, no?) or, as I think most people envision the missing link, between Human and non-human Animal?
Well, in the OP I gave all of Earth’s history, so the only prerequisite I think is that we have to know that it existed - so T-Rex is fine, but no dragons. Australopithecus OK, no bigfoot. So, you I suppose could bring back the ‘first species’ (which I understand we currently think was some type of prokaryote), although good luck determining when it first became distinct from the primordial protein muck.
On the ‘missing link’, the common ancestor of chimps and humans would be a good one (or going back a bit further, the common ancestor of all modern primates).
Another vote for the T-Rex. Yeah, I know there have been bigger ones found, like Spinosaurus, but there’s just something about a T-Rex that says, “Yeah, this bad boy should be stomping around in Washington, DC - right now!!”.
I want the new family sized meal bucket from KFD 
Imagine the size of the drumsticks!
So, which creature would I choose to bring back? Whichever one is the most delicious! 
Wow! Some fantastic responses! I’m still reading them, but wanted to interject mine… (And funny how many folks want to bring back a bird!)
If I really had to bring one individual from a species back, I don’t know if I could do it. I mean, is it really humane to bring back a creature that would live it’s life alone?
With that in mind, I’d definitely have to go with an extinct breed of dog, like say the Tahltan Bear Dog; they’re bred to corner bears and fight large cats, but they are still domesticated and do well with other animals.
Only if you have enough catsup! Or if they’re coated in toffee.
And at all costs, avoid the green wobbly bit!
That was my first thought too but, on reflection, a Pterodactyl would be awesomer.
Dodo was, by all accounts, not a good-tasting bird. They apparently died out not due to hunting by humans but the animals that accompanied humans to Mauritius (cite: Wikipedia:Dodo#Extinction).
Totally off topic, there was a Chinese girl adopted by an Amish couple (we’re very active in the adoption community, so I happened to hear about this). I would love to see & hear how she’s doing. Enculturation, that’s what I’m talkin’ about!
As you were, back to the discussion at hand.
Ahh yes, but when we genetically engineer them and bring them back, we will add in the all important Bacon genes.
I’d like to bring back the cave man for one day and study him.