To aru majutsu no Index : Great anime, although pay attention, the story jumps around a lot. From magic to science to vampires to alchemy to angels to espers to chalk-summoned monsters.
To are kaguku no railgun : If you liked Index, this is a slice of life spin-off following Oneesama and Kuroko and 2 of their friends. It has some plot in it, but mostly slice of life.
Elfen Lied : It's gory and involves naked people. If you are mature and can appreciate art and a great plot, watch it. Pretty emotional at some points.
Lucky Star : Was meh IMO, but it's just a typical slice of life with some lovable characters
Azumanga Diaoh : Really funny at some points, other points it's just typical slice of life. Characters are extremely lovable.