Here is a list of films which I thought 'influenced' the film: I don't think this is such a bad thing as people make out as it was like a sci-fi fan tribute film.
American landmarks in ruins: Planet of the Apes
Future Earth with litte plant life: Silent Running
Last person on Earth idea: WALL-E
Finding out you are a clone: Moon
Reality is not as you think: Matrix
A computer intelligence that is bad: 2001
An undermanned rebel army in the future: Star Wars
Sneaking onto the mothership to destroy it: Independence Day
Giant hovering ships over the planet: District 9
The Scavs stealth outfit: Predator
An oasis in an otherwise dead world: Mad Max
I also remember a Calvin and Hobbes cartoon where aliens came and sucked up all the oceans -OK that's a bit tenuous
That's off the top of my head, can anyone think of any more?