1. Code Geass: This so far is becoming a favorite of mine. I love the dichotomy of Lelouch's retributive form of justice with vigilantism, a sort of chaotic good alignment in sync with Suzaku's ethical approach of utilitarian justice of lawful good. Many of the issues discussed in this anime still have relevance.
Columnist Carlo Santos of wrote that the franchise "in a way, [...] reflects the malaise of a generation: the realization that old, rich, powerful people have screwed up the world and that the young are helpless to do anything about it". According to him, Lelouch's actions exemplify the wish to see problems like "economic, class conflict, political instability, radical extremism" solved by "Zero's vigilante methods" but Santos expresses doubt in such an approach and concludes that "the series is at its best when raising questions rather than offering a final solution".
I'm a political science major concentrating in world security and peace resolution so this particular genre interests me.
They also knew when to end the story. Unlike Death Note which comes at a close second, but honestly the whole Death Note plot died when L did. I wasn't satisfied with the ending to Death note. Code Geass knew when to close Lelouch's chapter. However, I do hope for at least some spin offs, I love the characters. Except for Nina. She was just annoying.
2. Death Note - I absolutely loved this anime! The animation was masterful, characters well developed and it seemed very realistic. This would of been my favorite if they ended the plot differently. L shouldn't of died before Light, it kept the plot thick. Again, I love vigilantist plots and the strategy genre, so this comes as no surprise.
3. Genshiken - this probably comes as a surprise to you. I found it hilarious however. Genshiken follows the lives of a group of college students drawn together by their shared hobbies, and the trials and adventures associated with being otaku. Kanji is a shy guy who lacks confidence and is a closet otaku. He joins a club and they take away his stigma of being an anime/manga fan. There's also a girlfriend who tis a self-professed otaku hater who tries to lure her boyfriend away from the anime/manga world. It talks about everything anime/manga lovers know about and their nerdy habits discussing subjects such as pilgrimages to comic conventions, otaku girls (me), video games, cosplay, and the hardly talked about doujinshi and hentai genres. It's dirty, nerdy, and funny as hell to any die-hard anime/manga fan.
4. NGEvangelion
5. Full Metal Panic
6. Gundam Series
7. Beserk
8. Gantz
9. unmentioned secret anime cult classic
10. Hayao Miyazaki Films. It was the first example of anime I ever saw.
There's a lot more I like but you said list just ten so there.
