1 for each category:

comedy
drama
action
horror
family
documentary
teen
etc.. and whatever you can think of

comedy - The life aquatic with Steve Zissou (does that count as comedy?)
drama - Leon
action - The matrix
horror - The hills have eyes
family - Saved!
Documentary - I don't know?
teen - Drop dead Gorgous

Comedy : Being John Malkovitch

Drama : The Elephant Man

Action : Run Lola Run (not really action, but a lot of running)

Horror : Ravenous

Sci-Fi : Cube

Family : Shrek

Documentary : This is Spinal Tap (well it's a mockumentary)

Teen : Thirteen

comedy- planes, trains, and automobiles
drama- match point
action- national treasure (I can't think of any I like)
horror- the excorcist ? ( I don't watch scary movies so I don't know)
family- home alone
documentary- yo soy boricua (rosie perez's documentary about puerto rico)
teen- ghost world or saved

comedy - the opposite of sex (funny but also sad, about life and sex with a fine performance from lisa kudrow)
drama - the myth of fingerprints (think closer if it's about a family, very sad and very slow)
action - the fugitive (an oldie but a goodie)
horror - mute witness (this is more like thriller but it's dark enough to qualify, still it's one of the best movies i have ever seen)
family - antz (i remember watching this cartoon about ants and being very impressed)
teen - election (it's hardly exclusively about teens but it's about high school life)