Everybody knows the frustration of dropping a cell phone connection. On long trips, especially to remote locations, it's likely to happen more than once. The solution is a satellite phone. Services like Iridium, Globalstar and Thurya provide coverage virtually everywhere in the world by using satellites to transmit signals instead of antennas mounted on earthbound towers.
A satellite phone is an especially good choice if you're going to be driving into areas where cell service may be spotty or nonexistent. The only restriction is that you need a clear view of the outdoor sky -- if you're at the bottom of a canyon, you may have to hike up to the rim for reception.
If you don't travel frequently enough to merit purchasing a satellite phone, you might consider renting one for your trip. Keep in mind that you'll pay more for calls, typically $1.69 a minute. Text messaging can save you some money, as they usually cost only 50 cents per message.