I just watched this movie (I really liked it!) and was absolutely amazed at how much I related to Tom. I have never encountered a character in film with whom I've felt such an affinity. It's uncanny.
Tom is DEFINITELY an NF. No doubt about it. And I'm almost certain he's INFP. It's how he "grew up believing that he’d never truly be happy until the day he met the one", it's in the way he values so preciously when Summer "opens up" to him, and it's how his values compel him to quit the greeting card company.
Summer, on the other hand, is an enigma to me. And, perhaps, that is the clue to her type. Their relationship reminds me of a relationship I had with an INTP. I wanted so desperately to "draw out" the side of him that I "knew" he had. It drove me crazy. I also see some SP "cut and run" tendencies in Summer, but (as others have said) there is quite a bit of Ne banter that goes on between them, and there is nothing to point to the ST pairing.
There were times when I thought that Summer was just a hurt and guarded NF. But then I see Tom at the end of the movie, jaded at one point, but bouncing back with the same NF enthusiasm for love with perhaps a bit more life experience to aid him in his next relationship, and then I realize that's more what a hurt NF looks like.