Most terrible anime tend to have pretty great manga in my experience - at least with shonen series'. The big three OBVIOUSLY aren't worth anybody's time watching, but (in my opinion) the manga of One Piece, Naruto and Bleach are pretty good - especially One Piece - mainly because there's literally no need for filler in them, and little to no recapping, which as people have said, tends to take up about half of every episode of said series'. However, even the Naruto manga seems to be stuck in a never-ending filler battle now...
And my worst anime experiences? A couple of them have been mentioned, but to reiterate, I tend to despise anything that reeks of being written for (or perhaps by) teenage boys that have a gore fetish.
e.g.
High School of the Dead - dear god, just disgusting levels of fan-service and all around mean spirited.
Gantz - I read the manga for a while, hated almost all of it but kept giving it the benefit of the doubt as I'd heard good things. I gave up after the level of gore-porn was taken to another level with that whole gunman massacre thing.
I also seem to just hate some things that people consider good:
Code Geass - absolutely terrible show. The plot is flawed in too many different ways and the characters are all totally unlikable.
Toaru Majutsu no Index/Kagaku no Railgun - I remember quite liking the first series of each of these when watching them when they first came out. I can't actually remember too much of Index, but Railgun was kind of nice though I only really liked Saten and Uiharu. Trying to come back to the pair of them recently, all I found was a pile of trash. I have no idea whether it was me or them that changed - and I can't entirely explain why - but I can't stand them now.
Finally, (good god, this has gone on longer than anticipated, I just have a hell of a lot of pent up ani-rage) there are shows that I loved which totally ruined themselves, and I'm thinking of one in particular right now:
Darker than Black - "This anime is great! Really interesting story, characters and powers. But you know what the first season missed? Obvious appeal for loli-perverts with a magical girl transformation!"