Mobile phone rental is almost always a bad idea unless you're never going to travel outside the US ever again. It used to be that you couldn't do any better than rent a phone in Korea or Japan since they use a proprietary mobile standard, but since they're now using 3G frequencies that many phones sold in the US can use that's not the case any more either. For Europe, Asia and Africa all you need is phone capable of using the 900 and 1800 GSM bands. If you've got a "quad band" phone so much the better as you're covered anywhere that uses GSM. Most countries have prepaid "pay as you go" SIM kits readily available at least in the city centre.