Hmm...
It depends on why he likes the movies he does. I wouldn't jump immediately into the deep and heavy stuff, it takes a while to acclimate to "OMG I care about a cartoon", but I can make a few suggestions.
For action:
-Full Metal Panic (not to be confused with the inferior and melodramatic Full Metal Alchemist). It's got good characters, lots of action, great animation, and giant robots which aren't done in a fantastically retarded way... I'm looking at you, Gundam. It's legitimately funny. Here's probably one of the best scenes:
He's not a nerd, he's a specialist
Also, it features some of the best American voice actors in the business, so it's definitely worth a look
-Martian Successor Nadesico. I hesitate a little to put this here, if only because it's improved a bit by also seeing Evangelion (of which it is a sort of expy), but it works on its own. It does tend toward grimdark stuff at times, but it's funny, heartfelt, and action-packed. Okay, so the animation leaves something to be desired at times, and it really is more interpersonal drama than pure "blow shit up", but it still works.
-Hellsing. It's kind of like the Halo of anime. Not a lot of real plot, and not much by way of character development. It's about a raging badass being a raging badass and looking damned cool doing it. Alucard, the most awesome vampire since vampires were created, fights with an organization whose goal it is to rid the world of other, less awesome, vampires. Be prepared for fan service, but not over the top, and significant amounts of blood.
For comedy:
This one is more difficult, because most comedy anime is probably going to be a bit too anime-ish for him right off the bat. Ouran Host Club (a review of which I should make eventually) is fantastic, but the animation style changes might get to him. It's pure slapstick most of the time, but it's good.
Negima!? (the punctuation here is important) is another good comedy series. It's one of the best dubs I've seen, and has some of the most amusing references out there. Lots of painting the fourth wall, and shout-outs to other things (including a South Park parody). If he likes any Monty Python, it's a lot of the same humor.
For Drama:
Probably the most difficult to find for him, because he hasn't been exposed yet to the "oh, right, I can give a damn about these people". Here's my best guesses.
Kare Kano. It's pure high-school romance, but very well done, and much more character growth than most shows in the genre. There's not much else to it, actually. It's about an overachieving boy, and an overachieving girl, meeting, falling in love, and learning to be mediocre.
Once he's more in a mood, and accepting of the idea of actually giving a damn about cartoon characters, you can branch out into some of the more emotionally intensive stuff.
Higurashi No Naku Koro Ni (When They Cry - Higurashi) is one of the best psychological horror shows I've ever seen. I can't do it justice in short form here, but just watch it at some point.