A few movies ive recognized AvPD characters:
Punch-Drunk Love (2002) - Adam Sandler in this film plays a character who is reluctant to date a woman one of his seven sisters set up for him. He shows himself as very nervous, sad and filled with lots of anxiety which could be seen as AvPD.
Heavy (1995) - Features what is most definatly an AvPD person, though never really described as such. A mid 30's, stout, pizza cook who lives with his mom who builds a unrequited love with the new employe at the restaurant, a very young Liv Tyler.
Rocket Science (2007) - Looking for answers to life's big questions, a stuttering boy joins his high school debate team. Not really AvPD, but i can relate to the boy's shyness and insecureness toward life and especially towards the oppisite sex.
Marty (1954) - Quite an old film, though its the earliest i can think of that portrays someone in their mid 30's, unmarried, single and unable to find love in his life.
Happiness (1998) - A movie with multiple plotlines and characters, Phillip Seymour Hoffman's character stands out as a lonely man who's only way to forget his misery is by making obscene phone calls, unable to come out and express himself to his attractive neighbor (or accept her less attractive neighbor's aproches)
These are the ones that come to my mind right now... ive probably seen more.