Some insecure apps and services use the UDID as a way to identify users. For example you can get some profile data from OpenFeint with the UDID. There are probably a ton of other small things like this, but overall I wouldn't worry too much.
And some secure ones used to use it for multi-factor authentication - e.g. you still username/password, but you can only do it on the device that you registered on.
However, use of UDID has been deprecated by Apple, and they are now rejecting some new apps that read it. You're meant to use a unique application-level ID instead.
