I've never seen any of the Star Trek shows in its entirety. Living in Central Europe, we had to wait years for new eps and one loses interest quickly thanks to that.
ST:TOS -> I've never seen the original series. Not even one ep. I did see some of the movies, though. But the series? Nope.
ST:TNG -> Ah, the series that I grew up with. I crushed so hard on Riker! He and Diana Troi are my OTP for this show and I started to lose interest fast once they turned their ship into a Riker-Troi-Worf triangle. I'm glad that they got together in the end, though :)
ST:DS9 -> Not my type of a show. The station was really dark and... metallic. The plot - too much about politics. I loved Dr. Julian Bashir, though. When his past and abilities were revealed, I squeed! But to be honest, I watched for his friendship with O'Brien. The rest of the characters didn't interest me much.
ST:V -> I fell hard for this show. Chakotay was my man, must've been the tattoo ;P I loved him and Janeway as a couple, but he and Seven of Nine? HOT! Like sizzling hot. What a great idea, these two together. Too bad that it wasn't explored more.
ST:E -> The most likable crew of all the shows, definitely. And Trip, Trip was simply cuddly! I was so pissed when they killed him off in the last ep. But! Then I learned about the official tie-in set directly after the show's finale. "The Good That Men Do" fixes the whole mess and twists Trip's death into a really awesome thing! So happy here.
ST: Movie -> Loved it! Like a lot 8)
You know, I'm a slasher at heart but in these shows, I shipped the characters in a very het way: Riker/Troi, Chakotay/Seven, Trip/T'Pol...
There's only one slash pairing in the ST series for me: Garak/Bashir. Those two... Wow! And Kirk/Bones in the new movie, of course, but that's another thing entirely... 8)