It was like a fictional proto-version of The Amazing Race, as I recall.
Anyway, the line between “cancelled because of poor ratings” and “cancelled because of a flawed or impractical premise” is getting thoroughly blurred here. I’m not sure where the short-lived Brimstone belongs, but I’ll mention it anyway since Alcatraz was cited and that show struck me as a blatant and inferior ripoff of Brimstone.
New Street Law - a programme about a small chamber of barristers, struggling financially but also struggling for clients and against a much larger chamber with apparently tons of rich clients and also dodgy legal practices (my take).
I loved this show and it ran for ?four seasons. The last episode in the last season aired involved a motor vehicle accident which was seemingly meant to be fatal to at least one of the main characters.
Then they took the show off and made no further episodes. Mongrels.
Kolchak: The Night Stalker. Rewatching it on DVD, I can see that it got kind of bad toward the end of its short run, but even bad, I want more of it.
Nah, it got cancelled for a way, way, way dumber reason.
Note: there is a site called IMDb where you can find out how long a show lasted. No need to guess how long it was on.
E.g., The Days and Nights of Molly Dodd lasted 5 seasons, 65 episodes. Which is why I was baffled by the OP. It started out great but if anything ran on too long.
Another vote for Terriers. Was it really just 13 episodes? Wow.
Carnivale. I hated it on the first go-round, but recently watched it on DVD, and freaking loved it. Should’ve been picked up for additional seasons by someone. Or HBO should’ve at least let the creator continue the story on with graphic novels or something.
Jericho.
Freaks & Geeks.
Chicago Code. I don’t usually watch shows as they air on networks (I wait til they show up on streaming or DVD), but I made an exception with this because my wife grew up with one of the actors. I totally got into the series, and was really fucking bummed as the season neared an end and there was talk of cancellation. And then it was cancelled.
Grand. This was a early-90s sitcom that I vividly remember loving. And then it got cancelled. Very quirky show about a rich family in the piano industry. Don’t remember much else about it.
Pushing Daisies and Wonderfalls are mine, although already mentioned. They did release the full anticipated season of Wonderfalls on DVD, and it’s incredible.
I didn’t watch the show in its original run because of the Biblical element but then caught up with it after, via Netflix DVDs. It was good and I would have stayed with it had it continued past that first season.
I was also a big fan of Freaks and Geeks and Undeclared (both Judd Apatow programs).
Terminator: Sarah Connor Chronicles Great show with a great cast. Lena Headey, Summer Glau, Thomas Dekker and Brian Austin Green.
It got offf to a rough start thanks to the Writers strike. The scripts were already written, but the strike prevented the producer/writer Josh Friedman from over seeing filming and editing of season 1. A lower level guy (that wasn’t in the writers union) did the job the best he could.
Season 2 was very, very good. Shirley Manson was brought in as a T1000 (the liquid metal terminator). Ended on a cliff hanger and then canceled. 
I heard there was a licensing conflict. The studio wanted to make movies instead of allowing a tv series. So fans got screwed.
I no longer watch Terminator. Haven’t seen the last two movies and never will. Greedy stinking studios can stuff it.
I have vague but fond memories of Maximum Bob–I’m thinking there was a married couple who described themselves as “brother and sister, once removed”?
Also Eerie Indiana, with the annual tornado, Bob, coming through and Elvis in his white cape and jumpsuit leading everyone in the shelter in singing Nearer My God To Thee.
One I don’t think has been mentioned is The Pitts, featuring a family with continual bad luck, i.e. the teenage daughter gets a VW Bug and it turns out to be possessed and falls in love with her and kidnaps her and takes her to Vegas to get married in a drive-through chapel. I was shocked to see it lasted 7 episodes; I thought it only made it through 4.
The Man From Atlantis.
Patrick Duffy, of Dallas fame, starred as a mysterious, amnesiac water-breathing superhero.
Battlestar Galactica : TOS.
The one great legacy of Terminator: Sarah Connor Chronicles is Shirley Manson’s recording of Samson and Delilah
awesome song. here is the show clip where its featured. Gives you idea of what we lost when they canceled this show.
You forgot Anna Friel. sigh :o
This thread made me remember how much I dug Misfits of Science. Even the theme song was awesome in an 80’s kind of way.
Q.E.D., an update of a Sherlock Holmes-type scientifically minded investigator in the present day.
and another vote for Misfits of Science.
Three of MOLLY DODD 's seasons were on Lifetime. Nothing on Lifetime or otherwise even remotely involving Nancy McKeon counts. 
Camp – About, what else?, but a summer camp. Had Rachel Griffiths and was a much more sweet coming-of-age Meatballs. I adored it. Only lasted one season.
Swingtown – Also just one season, sadly. But it had a great cast and was about 70s swingers. I don’t see what wasn’t to love. Plus, the clothes and set designs were awesome
Don’t Trust the B_____ in Apartment 23 – With Kristen Ritter and James Van Der Beek. I know lots of people tire easily of her, but this show cracked me up, especially with JVDB making fun of himself. First time I’ve ever seen a series air out of order and I knew something was wrong. One season here too.
The New Normal – Yeah, this tried way too hard and was ridiculously preachy, but I liked the message of inclusiveness it was trying to portray. And Ellen Barkin still looks good, even if it’s chewing scenery, and she only got to do it for 22 episodes.
GCB – About southern mean girls getting up to all kinds of shenanigans. Since it was set in Dallas and sometimes revolved around fundamentalists, I couldn’t wait to see if I’d catch even half of the in-jokes. This was the shortest in my bunch. It only had 10 episodes before being canceled. Argh!
Of all these, the only one that pissed me off beyond belief is the one I didn’t mention… I also watched My So-Called Life and it still rankles that we’ll never know if Angela and Brian ever finally hooked up. That is a travesty right there.
I loved lots of these. Firefly, Pushing Daisies, The Unusuals, Life…
I have Hulu. Sometimes it tricks me into getting into something with no future. It touted ‘A HULU Original!’. It was a show called Endgame, where a Russian chess grandmaster is stuck in a luxury hotel due to agoraphobia. He’s a genius and starts solving crimes by enlisting help from hotel employees and a chess geek to do leg work, ala Nero Wolfe.
I watched all 13 episodes before I found out it was a Canadian TV show that was canceled a couple of years before.
“The B____ in Apt 23” made me think of:
Selfie–Karen Gillan (“Doctor Who”) and John Cho (“Star Trek”). The show was really starting to click when it was booted.
Pearl - Malcolm McDowell as a snarky professor and Rhea Perlman as a working-class adult student. Loved the chemistry between the two of them (their characters couldn’t stand each other).
Cupid - the original one, with Jeremy Piven. Smart writing, great stories, cancelled way too soon.
Dweebs - proto-Big Bang Theory sitcom about a software startup full of nerds (including their socially inept, Bill Gates-style boss, played by Peter Scolari) that hires a pretty receptionist to help them navigate the real world as they prepare to go public. Great stuff, but only lasted a few episodes.