Loved James At Fifteen…but that was due to my then-unrecognized crush on Lance Kerwin…
My husband and I enjoyed Ringer from a few years ago. It should have been made more as a mini-series with a definite end. And Priest was awesome but pulled to its no so controversial for 2012 plot…the Sheepies couldn’t handle an Episcopal Priest with a gay son and a female bishop…I loved it cause I actually know people in much the same situations in our very liberal Episcopalian diocese.
Your mention of a 2012 series called Priest sounds like the 2006 NBC series The Book of Daniel, with a drug-abusing Episcopal priest, alcoholic wife, older gay son, drug-using daughter, adopted younger son, female bishop, and in probably the most controversial bit, the main character is regularly visited by Jesus Christ.
That’s kind of weird how the same show popped into our heads at the same time. At least you remembered the title 
John from Cincinnati. It was on HBO in 2007. I recall that I liked it a great deal, there was surfing, Garret Dillahunt one of my fav actors and I forget what else.
Studio 60 on the Sunset Strip another Aaron Sorkin show
Joe Doe starring Dominic Purcell as the protagonist with amnesia
Many of my favorites have already been mentioned.
Molly Dodd, Tru Calling, Doll House, Awake, The Unusuals, Journeyman, Carnivale, Kings, Life, Life on Mars
Mr Sunshine starring Allison Janney
I loved “Dream On”—I watched the boobie version on HBO—but I don’t think you can call it a show that was cancelled early. It ended with its story arc completed after six seasons and 120 episodes.
I’ll add my name to Terriers. The first and only season was great and it had at least one more season in it. I’m not sure if the concept could have carried it any further though.
I loved the first season of Twin Peaks, but by the end of the run, it was clear that David Lynch was no longer interested in the show, and likely had no long-term plan for it in the first place. I don’t think any more seasons would have produced anything watchable.
Heh 
This was a great Christopher Guest-led show with Chris O’Dowd, Michael McKean, Ed Begley Jr., and a whole bunch of other fantastic members of Guest’s improv troupe. It was really perfectly done. There was a brilliant sub-plot in which Chris O’Dowd’s sister had a sock puppet that everyone treated as a real person.
I don’t know if a second season would have produced anything more brilliant than the first season, but this one season deserved a lot more attention than it got. It was fantastic.
There’s one scene that still makes me laugh when I think of it. O’Dowd’s character visits an English farm hoping to meet distant relatives, and the cousin who runs the farm has a weirdly upper-class accent and hazes him like a public school boy. O’Dowd concludes that he wouldn’t like being a farmer because they “seem too posh.”
This is the Stephen Merchant sitcom spinoff of his Hello Ladies standup special. Most of the time, it’s absolutely bloody perfect with Merchant as a successful tech geek in Los Angeles who still can’t land a hot chick.
Merchant’s character is just so perfectly shallow and despicable, but it’s played just right and you have just enough sympathy for him. And Merchant is a genius at using pop music in the soundtrack. It really is a pleasure.
The final episode and the “movie” that closed off the series after it didn’t get renewed majorly fell down in character honesty though.
Based on the Geico Caveman commercials. This was a victim of unfair criticism, ridicule, and the writers’ strike. The show really was a brilliant sitcom lampooning racial tensions. And the acting—especially by Nick Kroll as a perpetual grad student and Julie White as a kind-of-racist apartment manager—was top notch.
I don’t known how much more can be said about these two shows. They really deserved more than they got.
This was also an unfairly neglected show of its time. A brilliant show-within-a-show parody of a Beverly Hills 90210-type teen soap production. This show got only one season while the horrible Nikki got a second season. (Probably because of boobs. Come to think of it, that’s not the worst reason in the world.)
“Sunshine” Cliff DeYoung, Bill Mumy, Meg Foster. I believe this was considered the first “dramedy,” and I also believe it was the first sit-com without a laugh track. Based on a superb TV movie, which spawned a follow-up TV movie (“Sunshine Christmas”), it was way ahead of its time. Funny and touching.
I thought of even more short lived series I liked.
Parenthood 1990 starring Ed Begley Jr, Thora Birch, David Arquette and Leonardo DiCaprio. Based on the movie of the same name this show sadly lasted only 12 episodes. It was far superior to the Parenthood 2010.
“The People Next Door” Starring Jeffrey Jones (Principal from Ferris Bueller’s Day Off) as a man whose imagination gets the better of everyone.
“It was HIS idea.”
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“Lou Grant” was yanked by the network despite (IIRC) good ratings and its rep as a CBS “prestige show.” Asner was rather vocal about some IRL political issue (I don’t remember what) at the time and the network fixed his wagon. Then Mrs. Pynchon fired him.
Two of my favorites, Battle Creek and Titus, have been mentioned. So I’ll add:
Lucky - a show about a gambler in Vegas. Good 30 minute show and casting Craig Robinson and Billy Gardell as the sidekicks was genius.
Reagan funding the Contras in Nicaragua, I think.
How could you possibly omit the delicious Kelly Rutherford as Dixie Cousins?
“Watching Ellie” with Julia Louis-Dreyfus. Like her in anything, but she was particularly appealing in this short-lived series. The clock counting down on-screen was a nice, unusual touch. She was always racing towards her singing gig, and the sometimes bizarre interferences made this show a delight. She’s a damn fine singer as well.
Another show that although it lasted three seasons, it was killed way too soon so it feels like it was short was Happy Endings. Great characters and funny writing.
On The Air, by Mark Frost and David Lynch.
Seven episodes were made, but only two were broadcast. I’m glad I bought the DVD before it became unavailable.
The 1987 British series Star Cops (a fairly hard sci-fi treatment of law enforcement in the near future, particularly among competing national and corporate interests in space exploration) had a somewhat stormy relationship with BBC2, leading to its cancellation after nine episodes.
Huge, huge fan of Freaks and Geeks here. Essentially nothing on TV has ever captured being a teenager like it did. But I think it would have gone downhill rapidly in a second season. The DVD set is really cool–the disks come in a yearbook.
I agree that Police Squad and The Tick were robbed. I don’t know how long they could have kept up that kind of hilarity but I would have liked to have found out.
I was ten years old when No Soap, Radio had its five episode run (“April 15, 1982 – May 13, 1982”) and I’ve never gone back to watch it again but it struck me as very odd by US television standards, and also very funny. Nominally set in a run-down Atlantic City hotel (Steve Guttenberg was the manager) it was stream-of-consciousness sketch-based comedy. Besides my brother, I have never met a single person who ever heard of the show.
I don’t know if 33 episodes qualifies, but I liked Brooklyn Bridge.
This reminds me that I was really into his show “Leap Years.” I think it was on Showtime and lasted 1 season.