What reasons should an app have to need my phone's International Mobile Equipment Identity number? I noticed that unreasonably many of ordinary apps have the "phone state and identity" permission. For example, Remember the Milk. What do they ask it for? Am I insufficiently paranoid?
Many apps use the IMEI for analytics purposes, for example counting users. Most tools like Google Analytics or Flurry need a unique ID per phone, so the IMEI fits quite well.
Note that this doesn't work on non-cellular platforms (like tablets), and the IMEI can also be faked: this is why some apps choose a different system (see this article).
It's often used to identify the unique phone, but often this is actually quite a bad idea. Most apps would be better off identifying you as a user, who can use multiple different devices on one account.