Depends on the carrier. I know T-Mobile has a BYOD (bring your own device) policy that will allow you to bring your existing device over. I think Sprint does as well. I know for sure that the bigger carriers - Verizon and AT&T do not have such policies.
It's not so much a question of if the second company will allow it, it's that the phone is locked to the first company and won't work on any other network. If you have had the phone for two years (when did that come out?), or bought it without a contract, then your current carrier may unlock it for you. If you are still in the contract period, you can't move it even to a compatible network. See this: http/www.tomshardware.com/forum/58384-36-need-unlocking-help-read-here