The biggest problem with Lost is that J J Abrams had a hand in it. He has a tendency to create shows and then either lose interest in them or pick up another project to pay more attention to.
SO FREAKIN' TRUE!! Damn you Abrams!

The first two season of Alias (another Abrams show) is to this day, some of my favorite hours of television ever. And then it just got SO bad. Heartbreakingly, why-are-you-doing-this-to-me bad. I think it had the biggest turnaround for me. Because the season 2 finale was so amazeballs and then season 3 was a trainwreck, and then season 4 and 5 were even worse.

The Office was ruined once Jim and Pam got together. And I loooooved Jim and Pam before they hooked up. Cutest will they/won't they couple. I don't know what happened but they really made Pam insufferable.

Heroes is an obvious one. First season was brilliant and then it became a confused mess.

I never really watched the first several seasons, but by all accounts 24 started off as a great show. By the time I started watching later in its run I thought it was just laughably bad. Del Murder kept watching out of some strange loyalty to Jack Bauer.

How I Met Your Mother is a terrible show. It's really really bad, but I still watch it because after so many years, I'm so invested. So I angrily watch every episode hating all these characters and wishing they would reveal the god damn mother already, even though I know that the reveal will never be good enough to make up for how bad the show has gotten over the years.

Weeds got terrible after season 2 or 3 (can't really remember). It kinda picked up again but those middle seasons were awful.

And the big one, Grey's Anatomy. Is there a show out there that can compete with the ridiculousness of this show? Not even science fiction shows like Battlestar Galactica (which totally lost its way too) can compete with the outlandishness of this one hospital. Main characters are totally brutalized on this show. Just a FEW examples:(SPOILER)

Meredith Grey: Almost killed by a bomb, drowned and saw ghosts before coming back to life, in a plane crash
George O'Malley: Hit and killed BY A BUS
Callie Torres: Thrown through the windshield of a car
Cristina Yang: IMPALED BY ICICLE. Seriously! Also involved in the plane crash
Derek Shepherd: Shot by a crazy guy, injured in the stupid stupid plane crash
Denny Duquette: Died and then became a ghost on the show. As a ghost had sex with Izzie, who in turn got skin cancer before exiting the show