I typically prefer to finish what I start. So I'm not one to quit a show I'm watching abruptly. That being said, there are a number of shows that I started but ended up dropping after awhile. To name a few at the top of my head:
Family Guy + The Simpsons
What I once found humorous just grew old and tired. The Simpsons earlier seasons are still golden, I'd watch those if I caught them on television and I've got nothing better to watch, but I couldn't say the same for Family Guy. That's just one show I get upset about watching because of how dumb the characters can be sometimes.
American Idol + X Factor
No more reality singing competitions for me, or any reality shows in general with the exception of King of the Nerds. I've grown weary of reality television.
Glee + Smash
I decided I would quit watching Glee when Season 3 ended. However, with nothing better to do at the time, I got into watching Season 4 and sort of enjoyed it. However, recently when I got behind on some of my shows, I just didn't feel like catching up on Glee and dropped it from my Watch-List entirely.
I actually wanted to watch NBC's Smash, another musical television series a la Glee, but I had the premiere episode sitting on my DVR for awhile that I eventually decided I quit. Season 1 was kind of a mess and even though they've seen to do a lot of reconstructing with Season 2, I just don't care enough to continue.
Digimon + Yu-Gi-Oh
After Season 4 of Digimon, I just stopped. My interest in Digimon was fading and I never seemed to follow up on the anime after that. Same goes for Yu-Gi-Oh. After the Battle City arc, I just never watched it again.