I can think of a couple:
Happenstance and Amélie, two French films about chance/destiny and interconnected lives in Paris starring Audrey Tautou. They couldn't be more different in tone and style.
Novocaine and Little Shop of Horrors to see dueling portrayals of dentists by Steve Martin.
Maybe Double Indemnity and Body Heat for classic noir and neo noir?
Close Encounters of the Third Kind
and
War of the Worlds
for two sides of Spielbergian aliens.
I still have fond memories of a great double feature at the Brattle:
Buena Vista Social Club
and
Genghis Blues.
And when I was a pre-teen, I remember a great cheesy environmentally conscious horror pairing:
Frogs
and
Godzilla vs. The Smog Monster.
Cheesy mutant animals on the prowl movies: Them! and Tremors would be good.
I have always wanted to do original film and homage double features:
I know Where I'm Going/Local Hero
Adventures of Robin Hood/The Court Jester
For those in the know:
Hudson Hawk / Long Kiss Goodnight
Oh, and I think Jess already mentioned
The Apple / Zardoz
Cheesy mutant animals on the prowl movies: Them! and Tremors would be good.
Them!
was pretty good, with the giant ants and all.
I love
Tremors.
That
would
be a fun double feature.
Robin Hood: Men in Tights
and
The Princess Bride
It's all Carey Elwes, baby!