I'm nearly 40 and have watched a lot of anime in the last few years

. There's a lot of junk (e.g. Speed Grapher, of which I could only stand to watch one episode), but a few shows definitely approach the level of high art. It helps if you understand the Japanese visual style and dramatic conventions, of course, which can be rather more sophisticated than those in Western animations.
Top recommendations:
1. Haibane Renmei
2. Azumanga Daioh
3. Boogiepop Phantom
4. Gunslinger Girl
5. Planetes
6. Fruits Basket
7. Genshiken
8. Niea_7
9. Gundam Seed
Of the anime shows I've seen, these should satisfy any intelligent adult who can overcome their preconceptions.
Mushi-shi may also warrant a spot on this list, after I finally see the whole thing.
I liked Hellsing, though it didn't live up to its potential. Chobits is good too, but I didn't like the fudged mystical ending, too often seen in this genre.