Why does an app read my phone's IMEI number? An awful lot of them do
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).