I have two with two different Sim Cards and tried it for you, no direct problem, but push e-mail will stop working, since if you're on BIS you can always only register one device. You will also probably have to re-send the Servicebooks each time.
So unless you don't mind registering the BB when you swap you'll be just fine.
Stupid counter-question: why would you want to do that?
Posted from my CrackBerry at wapforums.crackberry.com
Looks like you have a Storm through Verizon, sorry you can't put your Verizon sim card in other unlocked GSM Blackberry phones because it is CDMA, but if you have another Storm, that'll be a different story.