Surprised that Soul Eater hasn't been mentioned till now.
I'm currently watching Soul Eater. Art style and animation are great but the actual show hasn't been exactly gripping to be honest. It's only started to pick up and I'm at episode 12 so I don't find that to be a great sign.
Only suggestions are Gintama and maybe Psycho Pass.
Gintama anime always goes on breaks because they catch up with the manga. It also starts off really slow just so it can establish the world. After those first ten or so episodes it's just really awesome, arcs are not particularly long and most episodes are self contained with only a few references to past episodes every now and then. It's a sci fi/comedy that parodies almost everything, even itself, and one of the shows I'd readily say just gets better as you watch it. If it doesn't work out for you at first, it's okay. Just keep at it (you don't have to watch all of it at once) because it really does get good eventually.
Psycho Pass wasn't the great when I first watched it (it has a lot of potential but sort of just blunders aimlessly about halfway through) though the concept is interesting and I don't know, maybe it'll get better with the upcoming second season that's been announced.
I'd personally avoid One Piece, Sword Art Online and Ao No Exorcist/Blue Exorcist.
Sword Art Online, I'm pretty biased about this I'm not going to lie. I couldn't stand 3 episodes of this, too much stupid bullshit and melodrama.
One Piece is a one chapter = one episode basis from what I've watched, some people might prefer to just read since it's a lot quicker. I also didn't like the art style.
Blue Exorcist starts off great and then just really fizzles halfway through. It doesn't help that it has a filler/original ending. I don't know, maybe if you're interested in the movie this might be good supplementary material but frankly I just found it to be a miserable pile of disappointment. At least the art style is pretty too look at.
Other animes I'd stay away from are Eyeshield 21 and Majin Tentei Nougami Neuro purely because they are terrible anime adaptations and you are better off reading the manga.