Personally, FASA is my favorite non-canon interpretation of Trek. In many ways I like it better than the "real" Star Trek. My own personal Star Trek universe is mostly inspired by FASA. I have a lot of the old source books and a grip of the scenario books which I plan to adapt to a sci-fi universe of my own making, based largely on Star Trek with some nuBSG just for flavor. I was just going to run Star Trek, but I decided to do my own thing since a) I know what elements my players would enjoy that are not really present in proper Star Trek and b) a lot of my players are familiar enough with Trek that I wouldn't be able to tweak it at all without illiciting "that's not how it is" comments. Since I want to base it more on the FASA universe than TNG+ Trek, which my player's know better anyhow, I thought it better for us to do our own thing.
I'm currently using the Basic Role Playing ruleset by Chaosium Inc. Haven't actually played yet, but reading through it, it seems to be in similar waters to FASA's rules, at east, not much like D20, which I personally do not like at all.