or all u would need to do is get a new sim for the phone. which u can get from most phone shops if u want to go pay as u go.
if u want to go contract then there might be a few problems with that.
References :

Some companies such as Cingular lock their phones so if you buy a phone from them you can’t use it except with them. Unlocked phones can be used with any company that uses the same technology. for example nextel will only work with IDEN tech and verizon, sprint, US Cellular will only work with CDMA, TMobile, Cingular, CellularONE will only work with GSM. know what you are buying and what you need before you get it.
References :
I’ve been a wireless reseller for 4 years

There are actually a couple questions here. Unlocked phones as explained in some of the other answers refers to not having a "subsidy lock". A "subsidy lock" means that the wireless provider has had the equipment locked to their network in an effort to minimize financial loss when providing phones at a significantly discounted price or sometimes for free with a new contract. If you have an unlocked phone of the correct technology you can get it activated.
The second part about not changing your plan will depend on a few things. Primarily if your old phone is the same technology or not. Changing phone technology will frequently require changing rate plans. If both old phone and new phone are the same technology you should be able to switch phones. Be sure to notify your provider so they can note the new phone’s identification (IMEI) in their system. That will help confirm that data services will work correctly and if you carry insurance on your phone you can make sure the right phone is insured.
References :
former employee of major wireless provider