With AtLA, your mileage may vary. It depends on your definition of anime. I've typically noticed three main definitions:
Anime is Japanese animation. No exceptions.
"Anime" = Japanese for "animation." Therefore, all animation is technically anime.
Anime is usually Japanese animation, but can include works from other countries if they're up to snuff.
I'm somewhere between #2 and #3, and I most definitely consider AtLA anime.
In terms of manga, I'm also a big fan of Hikaru no Go, One Piece, Nurarihyon no Mago, Kekkaishi, and Skip Beat. I've never seen the anime for any of those, aside from a couple One Piece episodes.