only a small width would really limit what tyres you can get. most tyres can be stretched if theyre not far enough (this is a trick some people do over here to keep the tread under the guard to keep it legal). for 215-235, i dont think it would make much of a difference. for 245 and more, it would be noticeable.
just remember that contact patch only affects grip in wet weather, only the compound matters in the dry. wider tyres in the dry will only help it cool better, wont make it grip more (unless you're going from stretched to regular, then its noticeable in cornering).

@omgitsmatt - whats the width of the rim? should tell you on the inside.

@OMG.JAI xD - width generally doesnt matter, its more so the diameter of the tyre.

@Zdster - yup, dont need speedo recalibrated. all factory speedos are usually 2 degrees higher than the actual speed, so when your speedo reads 100, you're actually going 98 (a trick by car manufacturers to reduce the chance of collision). so if you bump up the rim size by the 2 inch rule, youll normally be getting your speedo spot on.