No, jailbreaking doesn't unlock the sim tray for use with any carrier. Some carriers will unlock them for you. Certain ones will only do it once you're out of contract. Otherwise, you can buy am IMEI unlock on eBay. They are really cheap and no jailbreak is required, but the phone must have been purchased prior to January 26th 2013 for it to be legal in the US.
Just to answer the OP's question... depending on the iPhone and it's firmware and baseband you can potentially use any SIM card with it. Once jailbroken you can install a package from Cydia known as Ultrasn0w (the 0 in sn0w is a zero), as long as your device has all the prerequisites then your unlock will work just fine. However, once you upgrade your devices software or need to restore you will lose your unlock.
As suggested above there are various methods available to obtain a permanent unlock. A simple Google search will suffice