It depends on the carriers and type of phone. The US has 4 "big" providors. Verizon, Cingular, T-mobile, and Sprint. Verizon and Sprint both use CDMA technology. Cingular and T-Mobile use GSM technology (along with most of world). The two providors with very interchangeable (not completely though) are T-Mobile and Cingular. I believe a large number of phones of Verizon and Sprint "could" be interchangeable, but they don't let you. Since each individual "phone" has to be provisioned within the carriers system to be used, they can effectively lock you out of using competitior's phones by not provisioning the phone to their system. CDMA providor phones and GSM providor phones are NOT interchangeable.
With GSM (T-Mobile and CIngular), the cell service is provisioned, not to the "phone", but to the "SIM card" inside the phone. This card can be moved phone to phone and the service follows the SIM. Unfotunately, there are still roadblocks to using carrier specific phones on another providor.
If the phone is locked to a specific providor, you have to first have the phone "unlocked" via a flash memory reset (assuming the phone is not purchased unlocked already). This "unbrands" the phone so it doesn't care who it connects to.
Another of the fine points are cell phone frequencies. The majority of the world (outside US) uses the 900 mhz and 1800mhz range. The US uses the 850mhz, 900 mhz, and 1900mhz range. Tmobile uses 900 and 1900mhz. Cingular uses 850 and 1900 mhz. Unless the phone is a "quad" band (i.e. V3 Razr) it will not support all the frequencies. It may still work on another providor, but by missing a frequency, it will tend not to work as well.
So what's this gobbledy glook mean? Basically, if you have Sprint or Verizon, no phone interchanges even though they share the same basic transmitting technology. If you have T-mobile or Cingular GSM, then the phones can be interchanged after being unlocked, but reception "might" not be optimal depending on your location and the type of phone.
Post what type of phone/service providors, and someone can tell you more.