Really depends on what you are looking for like if you want something with tons of action, something romantic and cute, hentai (pretty much porn in cartoon form), slice of life (something that reflects real life, usually accompanied by a romance story), or something with a little bit of everything. There are so many genres!
But here are some of my favorite ones:
Toradora!
Naruto
Pokemon
Fruits Basket (although the manga was much much better)
Full Moon (the manga made more sense and was more straightforward than the anime)
xxxHolic (both manga and anime are good)
Ouran High School Host Club (thought the manga was better but the anime was still great; it's very funny, even if you typically don't like this genre)
Hamtaro (it's old but it's about talking hamsters so what they hey!)
Doraemon
Hotarubi no Mori e (it's a movie but very good)
Howl's Moving Castle (also a movie and one of my all time favorites)
Spirited Away (award winning movie)
The Cat Returns
My Neighbor Totoro
Grave of the Fireflies (it's a really sad movie)
Sailor Moon (to some extent)
Kimi Ni Todoke
Yu-Gi-Oh
Koi Kaze (theme is of questionable morality for most people, but it's actually good regardless because the story was told really well to the point where you can say that it was cute and sweet)
And those are just the ones I can think of right now. Hope you go check some of them out if you haven't already!
