To use a local SIM card when traveling internationally, you must have an unlocked GSM phone.
Most U.S. mobile phones operate on a GSM (AT&T, T-Mobile) or CDMA (Sprint, Verizon Wireless) network. GSM is the global standard; CDMA is particularly strong in the United States.
But most CDMA phones aren't meant for global travel. There are exceptions, such as RIM's BlackBerry Tour, which operates on Sprint's CDMA network in the United States and on GSM networks internationally via a SIM card.
For maximum flexibility, get an unlocked, quad-band GSM phone. It will work on any GSM network in the world (there are four GSM bands altogether). Furthermore, it's not tied to a specific wireless carrier, as the iPhone is tied to AT&T's network in the United States.