If you like horror or mystery anime then I highly recommend Higurashi When They Cry. You'll have to watch it in Japanese, though, since only the 1st season is dubbed and the dub is terrible.
If you like comedies and don't mind watching really long anime then I recommend One Piece. If you want something shorter watch One-Punch Man.
If you like dark, tragic anime then I recommend Fate/Zero or Darker Than Black.