Comedy: There's a law that says I have to recommend Azumanga Daioh. Also, no guarantee you'll like it, but I personally enjoyed Lucky Star after the first 4 episodes. And try Haruhi, though it's not totally comedic.
Action: Maybe not for someone who's recently gotten into anime, but Nanoha, especially the second season A's. The first season doesn't really get good until pretty late, but it's awesome once it's there, and the second season is just awesomeness. The romance is confined to (extremely obvious) lesbian implications between the two leads.
Also, Baccano, Evangelion, Darker Than Black, and FMA (first series, Brotherhood is rushed) are excellent choices. On a somewhat (but not much) more artsy note, try Kino's Journey.