And then presumably have robo-children that look like dongs with wheels.
But wait, back up: What happened to all the other WALL-E-type robots that were left on Earth? We see their broken bodies scattered here and there -- why is WALL-E still functional when all of his brethren are broken down robo-corpses?
Easy: According to this theory from Reddit, WALL-E freaking destroyed them over a 700-year-long murder spree. That's why there's still so much garbage covering the planet after so long -- there was just one robot to clean it, and he's a psychopath.
Why It's Totally Possible:
First of all, just look at how casually WALL-E cannibalizes the parts of the deactivated units at the beginning of the movie -- he remorselessly rips the treads off of another robot to replace his own and hoards other spare parts in his trailer.
He totally poached that head from Johnny 5.
WALL-E is clearly a sentient being, capable of pain and emotion. He recognizes fellow robots as living beings (and of course falls in love with one). And yet, he doesn't appear to give the slightest fuck about desecrating the scattered corpses of his robotic kin. He's playing music from Hello, Dolly! as he tears their parts off. Apply the same thinking to human beings and picture a man who collects human body parts to wear and dance around in. Congratulations, you just imagined Buffalo Bill from The Silence of the Lambs.