Oh, I can’t believe I didn’t mention this before (or that another dozen or so people didn’t): Arrested Development. The only series I actually bought. Only three seasons and it is great. I suggest it just below Firefly.
Oh my god! Seriously nobody has even mentioned this yet? You said you wanted quirky stuff?
ARRESTED DEVELOPMENT!
It’s got an ensemble cast. Michael Cera! Jason Bateman! Will Arnett!
It’s too good for words, and it’s three seasons, so not too long either.
edit: I hear ya flight…I was wondering myself
I second Veronica Mars, having just finished the first season. (I know some people compare it to Buffy, but aside from being centered around a strong, blond high-schooler, they’re not that much alike. I’ve tried to get into Buffy, but I do feel like I’m too old to fully appreciate it—not so with Veronica.)
I would second Firefly but at this point it doesn’t need yet another person seconding it.
Another short (prematurely cancelled), quirky series: Wonderfalls. It doesn’t attain greatness, but it is fun.
If you like comedies, I’ll second Greg the Bunny and Futurama (which is definitely smart and well-written); and has My Name Is Earl been mentioned yet?
Veronica was a little cute for me. I don’t know, I guess it was pretty good. Maybe if I had watched it more. Some shows are like that, you need to see it every week and be “in” with it.
Boston Legal is like that. A show, btw, I highly reccommend. But you gotta know the characters. Work your way up to the “cow love” (I don’t recall the actual title) episode and you’ll be hooked. Or not. 
Always stay for the chat at the end.
I’ll mention, since no one else has (I don’t think) Carnivale, Dan Knaupf’s short-lived HBO series. Planned for six seasons, it only made it through two. That has positives and negatives for you; on the bright side, it’s just two seasons. To the left, though, the story arc had really only just gotten off the ground by the end of season two; in fact, viewed from the perspective of someone who’s seen the final episode, the first two seasons feel more as if they were meant to be a prologue to the real story that would’ve been told in the seasons to come.
That said: It’s dark and eccentric, though not gritty in the way Oz or even the Wire is–it’s a depression-era dust-bowl sort of gritty. It doesn’t hold your hand, though; you go into it knowing about as much as Ben Hawkins, the main character, and you figure it out with him, more or less. Characters are eccentric, mysterious, intriguing; I wouldn’t call them quirky because that feels a bit too light-hearted for most of what Carnivale was like. It’s not all gloom, but it does tend towards the creepy, weird side, in a Twilight Zone sort of way.
I liked it bunches, as you might guess, but obviously others didn’t, given its short run. YM, thus, MV.