GameFly.com rents both PSP movies and games.  (They're in seperate categories if you don't see them right away.)\n\nI've been a customer for about a year, and I think their selection and customer service are both stellar.  Ship times seem a little longer than Netflix, and pricing is higher (for good reason).\n\nI love the packaging (in addition to the Netflix style paper envelopes there's a hard cardboard shield) and I've never received a defective game.  The pre-owned purchase program is also a nice touch.
Is there anywhere that rents UMD movies for PSP?