When I was in college I discovered the bizarro psychedelic comedy film that is The Monkees Head. Written by Bob Rafelson & Jack Nicholson, Head came out in 1968, just as the pseudo-mop-tops were waning in their popularity. Sure they're a "fake" band, but that doesn't really matter. The movie is great and full of so many twists and turns with flashbacks galore, you don't know where you are and enjoy getting lost in its tom-foolery.
I have turned on many a friend to this film, and it even has a few good songs in it (courtesy of Carole King, Nilsson and a few of the monkee-boys themselves). When I lived in Philly, this was the sort of go-to movie we'd watch when we didn't feel like going out. I still have it on good ol' VHS.
Here's one of my fave clips: