This question is probably meant to concentrate on the TV series and asking me to pick between TOS, TNG, Deep Space Nine, Voyager or Enterprise but I'm going to cheat. I think my favourite incarnation of Star Trek is the movie reboot by J.J.Abrams. Much has been written about the 2009 film so I'll just say that it was a really clever and cool way to restart the Star Trek universe. I thought the casting was great, the action sequences and special effects were fantastic, and it even has a green skinned woman just like classic trek. I also didn't mind the shaky camera and constant lens flare that annoyed so many viewers.
It was neat to see Captain Pike in there and to find that he appears to have avoided his fate as shown in the Menagerie. And while on the subject of Pike I can recount a rather good suggestion by Simon Mayo that during the sequence of the film where Pike is being tortured by Eric Bana to reveal the Federation security codes, British audiences might amuse themselves by shouting at the screen "Don't tell him, Pike."
Anyway, I look forward to the next film in the new Star trek flavoured series.