Starting strictly Star Trek (because I adore alliteration)...
I always thought it would be awesome to date a Bajoran, but I'm not sure I want to be one. I find their spirituality and passion enthralling. I'm enchanted by their culture and their spirit more than any of the other races in Trek. But were I one of them, I think all that stuff would just be normal to me... and sitting and talking about the Prophecies would lose some of the captivation it holds over me.
Which I guess is a very orientalist way of looking at it... to say that I'm only enthralled by them as an "other".
Vulcans, also. I'd love to get to understand their culture from the inside. It's been said that Vulcans are actually the most passionate race in the quadrant and that their philosophy of logic is deceptive. It's not that they don't have emotions, rather that they choose not to live their lives guided by those emotions. But I don't think I could live like that.
I think I'd have to go with a Cardassian from Trek. Again, I find their culture fascinating, but this time thin I'd actually be comfortable living in it. The priority they put on loyalty is appealing. We usually only see it as loyalty to the State, but we've seen it demonstrated frequently that loyalty to friends and family supercedes even that. But, I guess it'd only be interesting if I could be doing something interesting. Maybe as a member of the Obsidian Order. Or as a Gul. You know, because nobody ever wants to be Dunar the Latrine Cleaner.
It's sorta like how "Time Lord" would probably be my default answer in general for if I could be anything from Sci-Fi. But when I think that, I'm really thinking of how cool it would be to be the Doctor, specifically. Or the Master. Being a Time Lord is only rewarding if you have a Tardis and the freedom to cruise around doing stuff with it.
Jedi isn't a race, so I can't say that. *laughs*
Oh! Or a Terminator. But only if my programming is completely unleashed like the one in T2, and I get to have a hot Summer Glau Terminatrix companion who also has an unleashed AI. *nods*
I might have put way more into this answer than was initially intended... >.>;;
Adding to... I think it would be pretty cool to be a Turian. Again, fascinating culture, very similar to Cardassians in their cultural values. I also just adore the Mass Effect universe in general. But, I feel like I want to keep it more humanoid.
And on that note, being an Asari would be pretty cool. Yeah, I'd lose my sense of gender... but I'd be a super-powered psychic hot chick that lives for 1000 years. Even if I don't become something awesome like a commando, I'd have enough time to dick around and write my own way.
Also, I completely ignored the obvious answer of Kryptonian. Assuming you're under a yellow sun, that'd be pretty boss... but since there are so few left, I'm not sure if that means I'd be more likely to get a chance with Supergirl by virtue of having compatible genetics... or less likely by virtue of probably being related to her. *laughs*