To name my favorite anime would take paragraphs upon paragraphs, something even I don't wanna read right now (and I am egotistical enough to go back and read some of my own stuff) I'll... Just leave a very shortened list.
(summary for each anime in spoiler so they can be avoided if you do not want to read, also Image heavy)
Tengen Toppa Gurren Lagann
Durarara! And Bacanno!
Spoiler for Summary:
seeing that both originated as light novels from the same writer, and have similar story style, I felt parring the two together was fitting. Durarara! Is the story about the many lives revolving around a section in Tokyo called Ikebukuro, particularly the mysterious gang, the Dollars. From the psychotically strong and short tempered Shizuo and the manipulative Izaya, to the mysterious Rider in Black, Celty, Durarara! has one of the most intriguing cast of characters, rivaled by few.
Bacanno! much like Durarara! is based not on a particular character, but a catalyst point, in this case being an elixir of immortality. The story, which jumps from timeline to timeline, can be confusing, but once the pieces add together, one would be hard pressed to be turned away by the time skips. Also, Ladd Russo is frickin' nuts, in an awesome way.
Oh, and Miyazaki/Studio Ghibli films... Seriously, nothing more needs to be said about that... Miyazaki rules.