I was never really exposed to Star Trek until I started dating Chris, who has a Star Trek shrine and owns every single series and season on DVD. A common date for us in our first year together would involve having sex like animals, then watching Deep Space Nine while eating whatever dinner I threw together to satisfy our sex munchies. It got to the point that "Hey, wanna watch DS9?" was code for "Hey, wanna fuck?" Fast forward to the present and we've been together for two and a half years, living together since March. We've finished DS9 as well as Enterprise and we're currently on the last season of Voyager.
In Star Trek, the petty divisions that exist in our time are gone. There is no discrimination. Now, just because there is no institutionalized discrimination, doesn't mean prejudism doesn't exist. An individual character can be racist, such as Miles O'Brien against Cardassians or Worf against Romulans, but that doesn't mean the Federation discriminates, nor is prejudism tolerated. Nearly everyone acts as an ally and will call out prejudiced behaviour whenever it occurs. That's not an unreasonable future to hope for.
So why am I a Trekkie? Because when I think of a future I'd like to live in, I can't think of a better one than what Star Trek shows. There's no discrimination, diversity is a fact of life, peace is always preferred over war, science and exploration are encouraged, religion is a personal matter and not public policy, and the economy is like communism, except it works. The human race has grown beyond nationality and is now working together as one planet, which is only a small part of a larger, galaxy-wide coalition. I know there are plenty of questionable things about Star Trek (faster-than-light travel, for instance) but isn't that vision of the future worth striving for? Even if we never achieve it it's a noble goal to shoot for.