My personal recommendations would include:
Lucky Star/Azumanga Daioh. Both very similar, and very funny. If you want something lighthearted and virtually plot-free that delivers on the laughs, go for one of these.
Sayonara Zetsubo Sensei. Another comedy anime with little in the way of plot, though the humor tends to be slightly darker than the above another one I'd recommend if you want a good laugh.
Fullmetal Alchemist. Popular things are popular for a reason. FMA remains one of my favorite animes; it blends genres extremely adeptly: there's action, there's drama, there's mystery; there's nothing not to like.
Higurashi no Naku Koro ni. Just finished watching this and its sequel series Higurashi no Naku Koro ni Kai. Without giving away important plot details, essentially each arc begins lightheartedly, focusing on the antics of a group of schoolkids, but gradually one or more of the characters starts to lose a couple marbles and, fueled by paranoia, turns the show into a delightfully twisted psychological horror. After the plot reaches its violent conclusion, it rewinds to depict a different series of events with the same characters. Easily my favorite anime since encountering it.
Pretty sure these have all been mentioned already, but figured I'd give them some extra weight if I could; I'm a big fan of 'em.
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