I have a lot of affection for this show and some of its characters, but I think people are overestimating its worth and quality when they say it shouldn't have been cancelled. There were definitely some brilliant characters, lines, sight gags, and full episodes, but I also think there were far more limp, uninspired episodes than really strong ones. I rented the DVD set to decide if I wanted to purchase it, and I was disappointed by how inconsistent it was.
It was certainly nowhere near the consistency of the best seasons of "The Simpsons" (although very few shows ever were), and looking at the series as a whole, I can see why it was cancelled. I could imagine people getting fed up with a dearth of weaker episodes and not sticking around long enough to see the better ones when they came along. On a more positive note, I have plenty of positive memories of this show. Most of the characters were really well-written and played. I wasn't so keen on Jay's son and sister (or any of the episodes about them), but his snobby mother and whackjob father were very funny.
For me, Duke was by far the best character on the show. I loved the jokes about Duke's ego...especially the one where he tells Jay how important it is to be modest. Then there's a cut to his hospital with a mechanically-talking statue in front of it repeatedly droning, "ALL HAIL DUKE. DUKE IS LIFE!". The movie parodies were spot-on too, and I'm appreciating them more now that I'm older and have seen more movies. Rene, thanks for posting that Arthur montage. Having recently seen that movie for the first time, I got huge kick out of it. I didn't remember the "Little Men" bit. It's too bad a lot of the perfect parodies were buried in rather dull episodes. I'm glad there's a montage of them on the DVD set.
My favourite episodes were the Siskel & Ebert one, the "Misery" parody, and the season 2 premiere ("Sherman, Woman, and Child"), which was definitely a huge leap in quality from the first season and showed a lot of potential for future seasons. Based on that episode (I agree with the earlier comment about Park Overall being a wonderful addition to the show), and the Siskel & Ebert episode, I believe the show had all the pieces in place to become something really special.
Unfortunately, I don't feel it ever got into the solid groove of a show you can rely on to deliver every week. This probably had something to do with its cancellation, but I know it had a lot of the same problems as "Futurama" too. It was mentioned on an audio commentary that the network could not provide a consistent time slot, burying the show and making it harder for viewers to follow. I may not consider the show an unequivocal success, but I do think it deserved better than that.