Even if you don't have International roaming on your mobile 'phone, here is a good reason to take your 'phone with you anyway ...
It's unclear which emergency numbers you need to use from a cellphone from various countries; the generally accepted norm for the UK is 999 or 112, 112 in Europe, 911 in the USA (other countries' emergency numbers vary).
Emergency numbers will generally work on the nearest available network and, usually, even with the keypad locked. Most sim cards will have world emergency numbers pre-coded so that travellers won't need to know the specific number for the country they are in. For example, 112 should automatically route to the appropriate emergency number for the country where the cellphone is dialling from.
*** UPDATE FOR HERTS July 2011 ***
Call 101 for non-emergency police matters.