you have a lot of subgenres to explore.

you can choose things like naruto, sakura card captor, bleach, full metal alchemist, pokemon. and so on. most of them have no end. (dragon ball is a classic, saint seya goes here)

also, there are psicologic ones like trapeze, evangelion, lain, noiseman, and so on.

if you like action and get cowboy bebop as example, you can go with black lagoon, hellsing, darker than black, gantz

OVAS, and short stories: FLCL (please watch it!), 5 centimeters per second, akira, rougin z, samurai x (ova only), here goes every movie like ponyo, chijiro and every gibli movie.

There is a subgenre for tematic and almost unconnected stories like mushishi, jigoku shoujo, mononoke, higurashi naku koro ni, paranoia agent

Long stories, berserk, tengen toppa gurren lagann (maybe this doesnt go here), death note.

there are a lot of anime out there, a lot of subgenres that i dont know of (like gore, or romantic, comedy, dorama, loli, etc) :P

Suzumiya Haruhi no Yuutsu its a genre for itself. a must see.