My favorite animes are a lot of the more commercialized stuff, mostly because I just havn't been exposed to a lot of the more rare stuff you guys seem to be really into, but I really like:
Akira
Ninja Scroll
Ghost in the Shell
Anything by Hayao Miyazaki (especiall Princess Mononoke, Nausicaa of the Valley of the Wind, and Castles in the Sky)
Cowboy Bebop
FFVII: Last Order
Pokemon (a guilty pleasure I had at one point myself Mrs. Lockheart
)
and Appleseed.
There is also some more Westernized animation which is inspired by the Japanese Anime which I am particularly fond of, including the Samurai Jack and Star Wars Clone Wars series, and the Animatrix compilation shorts. Some good stuff here.
And of course, Chrono Trigger deserves a special mention, even tho it is a video game I think it's still deserves to be considered an anime.