Well, as a standard rule, I strongly recommend The Melancholy of Haruhi Suzumiya for your anime viewing pleasure.

Now, onto business: You seem to be the type who favors action over romance or slice of life. If so, then my recommendation list would also include: Neon Genesis Evangelion (a must watch, it has achieved a level of fame almost on par to Dragon Ball), Full Metal Panic (all three seasons, especially fumoffu), Code Geass and Darker than Black. If you want a long running ongoing anime series that satisfies your weekend cravings for pretty much the rest of your life, I would recommend One Piece.

Also, if you prefer drama/slice of life/romance over combat actions, I would recommend Kanon, Air and Clannad.