I'd recommend some classic anime, myself. City Hunter, Lupin III, classic Dirty Pair, classic Bubblegum Crisis, classic Gal Force, Tekkaman Blade, Project A-Ko, The Enemy is the Pirates!, old school UC Gundam stuff, Nadia: Secret of Blue Water, Otaku no Video, classic Macross, Queen Emereldas and Captain Harlock, classic Record of Lodoss War, etc., etc….that sort of thing. Maybe it's just me, but the vast majority of what's coming out now just bores me to sobs and I find that I have much more love for the older stuff. Of course, that could just be my nostalgia talking.
For some newer stuff, I'll also say Samurai Champloo which is reminiscent of Cowboy Bebop only less bebop and space cowboys and more hip-hop and feudal Japan. Bonus, the main character has the same seiyuu as Zoro, Kazuya Nakai. Yakitate! Japan was also fun, and Karas is pretty to look at, if nothing else. I'll also second Berserk and Jojo's Bizarre Adventure, though as per usual the manga is better, and if you're looking for a cult classic fan favourite you cannot go wrong with the dub version of Special Duty Combat Unit Shinesman.
Actually, everyone should go watch the dub version of Special Duty Combat Unit Shinesman. Go. Go watch now. It is sixty minutes of pure joy.
There are a lot of other fan favourites as well that hail from the early to mid nineties, like Tenchi Muyo, of which I only recommend the OVAs and the first film, El-Hazard: The Magnificent World, anything Slayers, the Ah! My Goddess OVAs, Giant Robo, Irresponsible Captain Tylor, Neon Genesis Evangelion, blah blah blah. People say that Genshiken is great, though I'm not one to judge as I haven't bothered to watch past the first DVD despite actually having the box set. For girlier junk, Magic Knight Reyearth and Fruits Basket are worth watching, as is Mahou Tsukai Tai.
Then there are the films, like anything by Satoshi Kon, all of Ghibli's stuff, and other old school fan favourites like Akira and Ghost in the Shell or whatever. There's a lot to watch, really, and I can't even begin to list it all out.
~ jj ~