I never know how to answer this question. Too many great ones to really pick favorites, I guess.
I mean, the original Ghost in the Shell has a spot, because when it was all shiny and new, I somehow stumbled over it and that was really my big intro to anime. Plus the soundtrack and dark gritty theme are pretty schmexy.
Then there's Bebop. To me, there's a series you can point back to over and over when someone gets you to watch something that has no substance and say, "see how they did that? THAT'S good anime." It just has it all.. action, comedy, good characters, awesome jazz, some outside the box spins, and.. um.. Ed. Whatever exactly we wanna classify Ed as.
Lupin III, proving that you can again have great comedy/action/romance anime and it doesn't necessarily have to be new. The original is awesome, the new stuff is awesome, and has never managed to lose the feel. Great show.
In no really special order... Hellsing, Nana, Trigun, Bakemonogatari (didn't like the followup Nisemonogatari as much, but watched it anyways), Fullmetal Alchemist, The 11eyes, Elfen Lied, Trinity Blood, Jinzo Ningen Kikaida, Bodacious Space Pirates, High School of the Dead, Love Hina, Fate.. Enjoyed all those for one reason or another, and I'm sure I've forgotten a bunch and there's still plenty more I haven't even seen yet both old and new.
I have a premium over on Crunchyroll, and I've got several qued up that I haven't had the time for and/or are just barely rolling out, so maybe I'll find some more for the list, but yeah.. So much good stuff out there.
Really, about all I can say is if you're still mostly watching English dubs, stop that.
While some of the fansubs are absolutely horrid (and sometimes flat out wrong), at least when you have the original Japanese voices, the emotive sense tends to fit properly. Far too often the English speakers just fail completely to capture the proper feel for most of the characters, though admittedly, there's a few exceptions.
