Death Note
Not a thinking show. It's fantastic, it's my sixth favorite anime, but it's not a thinking show. The morality is black and white, and it has a strong, simple plot. The narrative is complex and loads of fun, but it doesn't ask you to think any more than Inception asks you to think.
Serial Experiments Lain
It might be asking you to think, but more accurately it's asking you to think at the level of its creators, which means it isn't so much a heightening of intellect as a lowering of intellect.
Ghost in the Shell
I wondered for a long time why people love Ghost in the Shell so much. Eventually I realized it's because it has the best title
of all time. If it had been named like...I don't know, just making up a name at random here...Mobile Armored Riot Police [http://en.wikipedia.org/wiki/Ghost_in_the_Shell], it would be resting in the pile of the hundreds of other decent sci-fi anime.
Code Geass
Why the hell not? I've realized that most of the people who like Code Geass like it because EXPLOSIONS AND TITS!!11!!!!!!!1!. I love Code Geass because it's actually smarter
than its creators. They thought they were making a great show and accidentally made a genius show instead. Which, naturally, is where most of its flaws stem from. Code Geass asks if there's such a thing as good and evil, but rather than asking "Is everyone evil?" it asks "Is everyone good?", and then asks that question not idealistically, but in a very cynical manner.
Bakemonogatari
It made me think about about how this is an anime I'd rather watch dubbed, because there's so much text on-screen at a time it's fucking ridiculous. It made me think about why Studio Shaft has a middle school girl fetish...okay, Madoka Magica made me think about that, too. Eh, sure, Bakemonogatari is a thinking anime.
Neon Genesis Evangelion
Pass.
Spice and Wolf
Really? Spice and Wolf? Well, I didn't know what the fuck was going on with all that economic stuff, so I guess in that sense Spice and Wolf is way smarter than I am.
Madoka Magica
Well, I think more thinking has been done
about Madoka Magica than anything except possibly James Joyce and a couple religious texts...
...so it probably counts as a thinking anime by default.
And I can't think of anything else in which a girl gets symbolically raped by a magic cat, so...there's that.
If I were to pick one anime to add to the list of thinking anime, it'd probably be...
Star Driver: Kagayaki no Takuto
Partly to troll all the "eva n gost n da shell r vrey srs bsns" people, but also because Star Driver is a really subtle anime...
It really delves into the question of what anime is and why it is the way it is. And sex. It's also about sex.