You are going to find a lot of GalCiv players on this forum.
Yes, it is a great game; it is easily one of the best games I have ever played, and would be well worth your time and money to pick up. It embodies the spirit of "one more turn", leaving you with many hours of lost sleep. The Game of the Year Edition is only $20, and is a bundle of the original game and the second expansion. If you are in Europe, check out the Expanding Universe bundle.
There is a demo available for it, but I don't know if there are any that incorporate the added features and game play options that came in the expansions. I also suggest you check out
this review/AAR, which though slightly inaccurate, is one of the best examples of how much fun the game can be (and is a hilarious article in it's own right).
If you are still reading this than stop right now and buy the game.