As you see, there are five shows all together, though people tend to forget about the animated one. To take a very general swipe, TOS is fun for its sixties styles, its rock-'em-sock-'em action, and the unrepeatable fun of being new and different.

The short-lived animated series featured the cheesy artwork of it's time, but was quite similar to TOS, even featuring the voices of the cast of TOS (I guess they couldn't find any work!).

TNG was a very popular update of the classic series, perhaps the most successful update in TV history.  An updated cast, along with vastly superior special effects garnered many awards during it's 8 year run. More emphasis was placed on relationship development between cast members than TOS, but still had it's share of action. You can also catch many a Shakespeare reference, due in some part to Patrick Stewart, who plays Captain Picard and comes from Shakespearean background.

Deep Space Nine was the darkest of the shows. The crew lives on a station right next to a wormhole (a space anomaly which allows travel to the other side of the galaxy). They're currently fighting a horrible war with a race of shape-shifters, and the captain is a religious figure -- or ambassador to the aliens who control the wormhole, if you prefer. Confined to a space station, emphasis was placed on the war and the small planet they were assigned to protect.

Voyager is the latest and most character-centric of the shows, focusing on the lives of a crew of 140 or so originally stuck 75 years from home. The episodes deal with the crew's need to get along despite the fact that some of them aren't "real" Starfleet, and give us brief looks at aliens and cultures which the ship passes by.