There are tons of Anime I watched that aren't very good. But I'm not gonna get mad about YuGiOh (which I recently rewatched, because of nostalgia), because it is very clear what type of show that was. The ones that truly aggravate me are the super pretentious ones, especially when they are hyped as this deep meaningful piece of art. With that out of the way:
Neon Genesis Evangelion
Good looooooooord, this anime was a waste of time. I never got why everyone loved it so much. It is sooooo boring. It never gets around to telling the story it promises, the characters are unlikable, boring or both, the judeo-christian symbolism doesn't make a whole lot of sense and the animation budget was clearly non existent. And the ending (both of them) are just so unsatisfying.
I get a lot of people telling me that I just don't get it. But that doesn't really matter all that much to me. If a story is told so that a vast majority of the audience won't get it without extensive research, it's probably not told to well. So if the message is lost the story should at least be somewhat enjoyable, which NGE wasn't at all for me. Ugh, I really hate this thing. And the fact that it is so popular will haunt me for the rest of my life 
Ergo Proxy
Ergo Proxy suffers from a lot of the same problems that NGE has for me: Interesting build up for a story, but no satisfying resolution, disjointed story telling for the sake of disjointed storytelling and dull characters. In the case of Ergo Proxy I'm probably more annoyed at myself for sitting through it instead of quitting
The saddest part about this show is, that it could have been really cool. It has a lot of interesting concepts for it's world. But the characters never really interact with it in a way that uses this potential. Instead we have weird episodes, where really important plot points are presented in a game show format (thus having no emotional impact on the characters or the viewer) or we spent time inside a characters head without actually progressing much. *sigh
Thing is: I like deep philosophical Anime, when I can get it. Ghost in the Shell comes to mind, which I love. Or Monster, where complex moral dilemmas are posed without the Anime outright telling you a solution. It just frustrates me to see potential wasted.
Wings of Honneamise
Beautiful animation, no clear idea for a story. I wouldn't put it on the worst list if it weren't for the weird relationship between the main character and the woman. Having her apologize to him after he tried to rape her was just disgusting to watch.
