Mike is right for a GSM-based phone. Get an unlocked one (make sure it's really unlocked, some on EBay claim to be, but are not), and move the SIM chip. No one will know. Cingular & T-Mobile are the GSM carriers.
For Verizon, you can pick up a phone on EBay or otherwise, but you must make sure it's compatible with VZ. You can go onto their site and enter the new ESN... the site will ask you why you're changing (phone in for repairs is a good answer), and it will activate on the system within a few minutes.
I have no idea how Sprint or Nextel handle it.
More important, IMHO, than the lesser minutes on the plan is the fact that you're off of contract, meaning you can bolt anytime. The reason the carriers want you to sign a new contract with a new phone is just that: they know they've got you, and they want to keep you on a contract so you don't leave. Such contracts are very one-sided, and ought to be illegal. Again, IMHO.