I like character driven drama that is the characters are more important than story - I think DS9 and Voyager were the best for that - I will give the nod to Voyager - Though in all honesty the thing I remember about the ST series was in each franchise from NG to Voy, I would connect with some characters and hate others. For some reason I never really took to the Orig or Enterprise.
Once TNG hit its stride, it was incredible. Like @Avenuewriter says, the first two seasons were pretty bad and pompous (the Mad Magazine satire was written based on this and shows them as a bunch of whiny do-gooders) and pretty much brought the whole franchise up to date. It felt smart, flashy and futuristic yet believable.
DS9 I didn't really like enough to stick with it. Sisko was like a boring, moralistic uncle who'd send me to sleep. It seemed to be too much about wacky aliens and culture clashes, and so I didn't last long enough for the Dominion War to start which is apparently when it became 'good'.
Voyager... had potential. It seemed to be a bit too much of Delta Quadrant races being impressed by how generous/kind/adaptable the humans were. I don't know, it just smacked a bit of a starship from Planet USA arriving and showing them all the 'right way' of doing things. I've seen quite a bit of it thanks to reruns, so I think overall it's pretty good.
Enterprise was literally Planet America sending out a starship to tell aliens to stop being so mean to each other. That Archer figured he had the moral high ground when he was basically showing up ignorant into almost every situation just made it funnier/more cringeworthy. Tucker at least seemed like a real person, I remember when it first aired, everyone was obsessed with T'Pol's nipples and the decontamination gel.
This just leaves... TOS. Ah, purple sand and styrofoam rocks. Because they couldn't often show other ships or starbases or anything else, you really did feel they were out there on their own. It was pretty obvious that they looked at what was being made on the adjacent soundstage (a cowboy/gangster/Nazi/Biblical picture) and decided that the Enterprise had miraculously encountered yet another planet that had paralleled Earth's development and history. There were a few cool storylines that were thought provoking, like when they find a planet that happens to be still another alternate earth, but one where the last vestiges of Chinese civilization hunt down feral Americans after an apocalyptic World War 3, but generally it didn't really feel like exploring space and meeting aliens so much as it did doing a lot of drugs and finding beautiful 1960s people to have sex with.
The Original Series is my favorite by far. Best episodes, best movies, and the series that started Star Trek so you can't beat it imho.
TNG is okay around when they introduced the borg, basically the first two seasons are generally terrible. Too much "humanity is teh awesome" and a lot of pompous characters.
DS9 is okay, I never got into it that much but it wasn't terrible either. However, Sisko is totally badass.
Voyager is absolutely hilarious. In that it's 7 seasons of wasted opportunities. If you're a fan of Trek, see if you can find SF Debris' reviews of Voyager because they're a barrel of laughs that point out how terrible many of the episodes are.
Enterprise practically killed the series, while there might have been some okay episodes, it doesn't change the fact that this series was terrible.
Although I have never seen a ST episode from any of the shows, I have watched movie reviews and video scenes for Next Generation. + I'll give NG the vote simply because of the origins for one of my favorite memes. http://i.imgur.com/iWKad22.jpg?fb