This creates a great opportunity for people who are not satisfied with their offers or just want to switch for example from contract cell phone service to prepaid service operated by other carrier. The procedure is very simple and usually once you transfer the number, your old service will be automatically disconnected. However, you should remember that if you have a contract type cell phone, then you may be still required to pay fees for it.
If your carrier doesn't want to help you with porting your phone number to other company, you can always complain to FCC and ask them to take steps against them. However, this is a very rare situation and in most cases everything will be done without any problems or complications. You should also remember not do cancel your old service until you know that the new service is ready and process of transferring your number has began, since you may have lose access to your old number and hence you will not be able to transfer this number to the new carrier of your choice.
The whole process of porting a phone number from one carrier to another can take up to one week. In some cases it can take slightly longer, but usually the procedure is finished within a few days from filling a request. Once you receive the notification that your number has been transferred to your new carrier you can disconnect your old service without worrying that you could have lost access to it.