If you are asked for your SIM number by your carrier or mobile phone operator, you will find this on your iPhone within Settings: General: About and scroll down to the bottom. The IMEI is the unique number for your phone (International Mobile Equipment Identifier), and the ICCID identifies your SIM card (or the micro SIM, in your iPhone 4). When I was on a live chat with a Vodafone helper, he didn't know what I meant by ICCID - so this is worth you knowing!
These instructions still apply for Apple's new operating system iOS 6 (released in September 2012), so are probably also correct for their newest phone. If you need to know the ICCID for your iPhone 5, just follow the above directions!