My brother and I were trying to come up with movies that would fall in the "Slice of Life" genre. Any come to mind?

Just off the top of my head:

Killer of Sheep
Junebug
George Washington
Wild Tigers I Have Known
YiYi
Scenes From a Marriage & Saraband
L.I.E. & 12 and Holding

Quite a few of Eric Rohmer's films easily qualify as this, too...