Before I return to examining the myriad of living creatures that have already gone into space, this whole theme got me thinking about animals I would like to see go into space... if we had all the time and money and room:
Woodpeckers. Given modern metallurgy, these ought to be way less trouble than the ones on Noah's Ark. Can't imagine what a loose one might get up to on the ISS, but I say we throw a few up there to find out. Actually, I'd love to see any bird in space. Would it be able to perch, fly and sing properly after adaptation? We've observed egg development and hatchlings, but so far no weightless attempt at "flight."
Penguins. Flightless, waddle-whap lump of flap-doodling lovely. That would just be fun to watch.
Meerkats. Okay, technically they are mongooses... which reminds me that we should also bring along...
Snakes. Could they adhere to surfaces or would they float right off them unless wrap-coiled?
Any Marsupials. We have yet to send any marsupial mammal into space, and there are some great light-weight ones to choose from.
Bats. Hmmm, echolocation, anyone? Would it be thrown off? One particular bat tried to hitchhike to the ISS, but that didn't turn out so well.
Octopi. Any animal with three hearts, well, that would be incredible to study in LEO. We wouldn't exactly have to worry about bone loss, since they have no bones. And maybe one of them can predict when we will finally make it to Mars.
Otters. Would they be able to do that death-by-cuteness somersaulty thing in micro-gravity?
Of course, most of these are just fantasy, particularly for any animals over a few pounds. We'll never know, for instance, how elephants or tigers will react to micro-gravity. By the time we invent the technology necessary for propulsion, or even a craft large enough, such species will very likely be extinct.
Crews don't normally have time or room for any animals who require a great deal of upkeep. Laws governing day care centers for Homo sapien young are nothing compared to the NASA standards for animal housing, as well as the regulations set forth by the Public Health Services Policy Act and the Animal Welfare Act.
Live payloads also provide a challenge for ground crews. We've all seen instances where launches have been scrubbed over and over again due to weather or other launch-window factors. Imagine having biological packages scheduled for a Shuttle mission where you had to care for, load, (launch scrubbed), unload... care for, load, (launch scrubbed), unload... care for, load, (launch scrubbed), unload... yikes.
If you were headed to the space station, which pet would you take?