Off the list:
Ao no Exorcist: ★★★ Decent. Watch it if you've got nothing else to do.
Bleach: ★★★★★/ ★★★★/ ★★ - First rating till the end of Soul Society Arc. Second till the Arrancar arc. Third for the shite served after that. If you plan on watching this, just skip the
fillers, starting with the Bount Arc. If you aren't hooked by the time Byakuya blitzes Ichigo (episode 15-ish), then this isn't for you.
Gintama: ★★★★★ I don't know how to describe it, but just give it a try. You won't regret it (probably). Superfun.
Ghost in the Shell: ★★★★★ Almost as good as Akira.
One Piece: ★★★★★ Best of the best as far as shonen anime go, takes a while to get going - most people get hooked by Arlong Park Arc. Caveat: It's suuuuperlong, so watch it only if you've got loads of spare time.
Magi: ★★★★ Really good. But the childish drawing style turns people off.
Rurouni Kenshin: ★★★★★ Top 10 anime of all time, must watch - including the OVAs. Not very funny though.
Mushishi: ★★★★★ Mushishi is art, but not everyone likes it. Doesn't have a distinct storyline, essentially it's a compilation of small storylines with mushi and Ginko as the sole common element(s).
No Game No Life: ★
Steins; Gate: ★★★★★ You might to persist with this one because it's relatively complex, and the first 4 or 5 episodes are weird. One of the best anime of recent years.
Another: ★★★ Decent at best.
Fairy Tail: ★★★ One Piece knockoff.