They're only songs if they're sung, you know. These are pieces of music, compositions... 'themes' would suffice. (Include the lyrics Star Trekkin' and the TOS theme qualifies, anyway...)
1. Star Trek: The Next Generation - Pretty much the definitive theme as far as I'm concerned. It's one of Goldsmith's finest works, and it's certainly a few shades above his collaboration with Jay Chattaway in -
2.Star Trek: Voyager - the horns are a tad nasal. But generally, this is a superb theme, sweeping and majestic. Still one of the best around.
3.Star Trek: Deep Space Nine (1-3) - Dennis McCarthy's music for Star Trek has never sounded particularly inspired, it's by-the-nubmers symphonic fluff. But he gave us easily his most evocative and haunting theme with this piece.
4. Star Trek: The Original Series - upbeat, carefree, and flighty fun, suggesting in all its innocence the vastness of space in the first few bars. Still a classic.
5. Star Trek: Deep Space Nine (4-7) - The same thing as the earlier one, but without any pretense to being haunting or evocative. It makes sense in context, and it's an okay theme. But 'okay' is about it.
6. Star Trek: The Animated Series - A bit goofy, but rather charming. The best piece of music associated with this show, which often relied on its handful of cues too extensively.
To rate the remaining one might leave people the impression that I like it in any sense; or perhaps at least that I consider it a mode of musical expression; thus it is best to pass over it in silence.