Note: Apple will no longer accept apps that access the UDID of a device starting May 1, 2013.
Instead, you must use the new methods identifierForVendor and advertisingIdentifier in iOS 6+ for accessing this. See related post here for more detail.
Old way (deprecated and will result in App Store rejection)
NSString *udid = [[UIDevice currentDevice] uniqueIdentifier];
As of iOS7, the uniqueIdentifier property is no longer available.
See the UIDevice reference.