Firefly is an excellent choice, of course. The reasons to like it have been discussed on here before, so I'll skip.
I saw Twin Peaks mentioned on the Question Thread. That's good, too, but it's been a long time since I've seen it, and am not sure my specifics on that one would be at all helpful
Deadwood and Rome - the stories are well written, the characters are downright juicy, and the production quality will put you in the middle of it all.
Dead Like Me - Stories are good, characters are quirky, and it's got a likable morbid humor.
I know you're criteria for series which are complete, but I think Dexter might be a good exception to the rule. Each season has a definite ending - no cliffhangers. It's like watching a novel.
Most of the other long time series I watch are sci-fi, so I'll skip those. When it's wrapped up, you might want to give Battlestar Galactica a try. It's sci-fi, but that's not "the one thing". It's war, the end of everything, and watching what happens when people actually do lose everything. Deals with what makes one human and civilized. Looks at the best and worst in people, through religion, tradition, politics, relationships...