Star Trek is a bit of an odd duck in my RPG collection. I tend to roleplay to explore different mindsets, more exploratism than escapism, so I tend to prefer settings with a moral different from ours and not have characters matching our modern values (unless it is our world with a twist, like Buffy or Star Gate). I just don't want to feel that the game makers, or the people around the gaming table, share any of the values we might explore in the setting (which might be things like sexism, racism, homophobia). If I roleplay i Roman, I want to argue what is the right way to handle slaves; not playing someone opposing slavery.
Star Trek is a culture I would like to live in (well, I wouldn't mind having access to the technology as well ). The UFP has its flaws as people has flaws, but it is fairly free of the prejudice people still are suffering from in our own world. In Star Trek, I feel I can explore things from my own point of view. A conflict isn't won by a fight, but by understanding the opponents way of seeing things and find a solution. Sometime, force has to be part of the equation, but never the solution.
So... What is it about Trek that makes you want to roleplay in it?