I absolutely adore this film, are there any others like it?

I this film is harder to compare to others. But this film reminds me of

Buddy: The main character is a shy, socially akward, religous young adult whose next door neighbor falls in love with him. The main character in this has a fair share of mental issues. He also has a wierd family dynamic.

May: The main character is a female who is very shy, socially akward and she falls in love with her a man who comes into her job one day. She's very lonely and isolated. She also changes like Barry from shy and unsure to assert and confident in the later half of the film.

You'll definitely want to check out the Big Lebowski if you haven't already.

Punch-Drunk Love is truly unique. But in the vein of unusual or alternative love stories, there's a Korean film I really love entitled, Oasis:

http://www.imdb.com/title/tt0320193/

Check out Hal Hartley's films from the early-mid '90s - Trust, Simple Men, and Henry Fool to be more specific. They may not fit your exact criteria, but you still might find the feel you're looking for.

Plenty of great suggestions here, but I'd like to suggest something a little out of left field: "Joe Vs The Volcano".

No really, give it a try! Though it branches off into its very own brand of absurdity, the surrealism of the first half of the film is, in my opinion, very similar to that of "Punch Drunk Love". It is a visceral atmospheric connection that occurred to me in the theater while watching "PDL", I suppose spurred on by the opening scenes of someone trapped in the ridiculous automation of humdum consumerism, and a nonsensical one-sided telephone conversation. The phone call was really the clincher for me - as a huge fan of the largely unseen "Joe", I've noodled with the idea of how cool it would be to make another film that starts off with the other end of Waturi's conversation. You'll know what I'm talking about if you give "Joe" a try, but suffice it to say that upon seeing how "PDL" started, my jaw dropped as suddenly it seemed that someone had actually done this! It's not of course, but for me it's close enough to tie the two films together. Check it out!

Many Bothans Died To Bring You This Information

The greatest love story that I've ever had the pleasure of viewing. Definitely one of the best films I've ever viewed.

Thanks for the recommendations everyone. Sorry it's been so long since I replied, but I have had the chance to watch at least half of these movies and looking forward to the rest. But one film in particular that I saw on my own was the 1986 David Lynch film Blue Velvet. Man oh man, that movie has crazy similarities, like the way the camera pans away in some scenes, the strong colors, the surreal dialogue, etc. It is just awesome! I've never been a David Lynch fan either haha

I saw this movie for the first time today. Frankly, I have never been a fan of Adam Sandler but I liked Punch-Drunk Love. It had the feeling of "The Trial" starring Anthony Perkins and Jeanne Moreau. There are no similarities in plot, characters or settings, but the main characters suffer from their "outsidedness." Sandler and Perkins were surrounded by drama that they wanted no part of and from which they could not escape. Punch-Drunk is certainly not a comedy - I don't know why it is billed as such. It is what used to be called an "art" film.