I am doing some research and would like some recommendations for two types of films (preferably those available on DVD).

The first is films that feature in-depth and honest portrayals of romantic relationships. I am thinking along the lines of HBO's Tell Me You Love Me and perhaps, in a stylized way, some of Godard's films, especially Contempt and Pierrot le fou. Really any film that has moments of particular insight into romantic relationships will work. Even the recent film The Breakup had its moments, such as when Jennifer Aniston's character attends a concert by herself and then goes home and cries. At the same time, that film bows to certain mainstream conventions that work against its otherwise honest intentions, so I'd consider it a borderline case.

The second is films with loose, very simple plots and episodic structures that deal with the reality of one or more character's daily existence. This of course describes Bicycle Thieves and many other Italian neo-realist films, and I have seen many of those. It also describes some of the contemporary progeny of those films, such as Man Push Cart. Any other examples are appreciated.

EDIT: I should add that I am not looking for documentaries.

Thanks in advance for any recommendations!

in regards to the first type of film you're looking for: 'all the real girls' (2003)

1st type of film: A Nos Amours, Brokeback Mountain,
2nd type: Umberto D

Love and Sex with Jon Favreau and Famke Janssen is a good one for the first category.

Added the ones I haven't seen to my Netflix queue. Thanks for the recommendations. Any others?

1st category: Your Friends and Neighbors The most honest "relationship" movie I've ever seen.

Closer is a good film for relationships. Don't know quite what you're looking for the second type of films you could check out La Haine which all takes place in one day.

1st type:
Say Anything...
About Last Night...
Before Sunrise
Before Sunset
When Harry Met Sally
Singles
Chasing Amy
Sideways
Rocky
Sex, Lies and Videotape
Threesome
Fast Times at Ridgemont High
Moonstruck
Sea of Love

2nd type:
Clerks
Kids
Groove
Spun
MacArthur Park
Baby Boy

not really sure if those were the kinds of movies you were looking for.

For the first type: Annie Hall

For the second type: Barfly

1st: Friends with Money

For the first one I'd say Swingers.

I mean there really isn't any actual relationship I guess, but poor Mikey reacts to his breakup in a way I'm sure a lot of guys have.

Some very nice recommendations here. I've seen many of the movies listed and was reminded to see others. Keep them coming, thanks!

1st: The Shape of Things, Who's Afraid of Virginia Woolf?, Eyes Wide Shut, Wings of Desire, Manhattan, Eternal Sunshine of the Spotless Mind

2nd: Morvern Callar, Stroszek

For the second one "American Job" came immediately to mind - Chris Smith's first movie

1. Mulholland Drive (since the movie is basically a deconstruction of a single womans desires and intended actions vs. the horrible reality of her actions)

2. Not sure if it's episodic, but The Station Agent fits imo.

Yes, I loved The Station Agent. Good call on that one.