If you were going to try and watch them in a chronological order, this is the order you'd want to go.
Star Trek: Enterprise
Star Trek (the original series)
Star Trek I-VI (movies)
Star Trek: The Next Generation
Star Trek: Deep Space 9 / Voyager / TNG movies (all three sort of ran concurrently with one another)
Star Trek (new movie) - Because of the events of the movie, you'd understand the reasons why I put it at the end (to avoid spoilers).
If you were going to watch it just to try to get into the franchise, then I'd go with the original series and TNG, then go with everything else after (just because I find them the strongest parts of the franchise).