As the other answers say, $USER is usually set to the name of the current user account.
But at least on my system (Ubuntu 14.04) the $USER environment variable is not set for cron jobs. Instead, you can use $LOGNAME (POSIX), which is part of the environment for cron jobs.
According to the environ(7) man page (type man 7 environ or man environ.7 to read it), $USER is used by BSD-derived programs and $LOGNAME is used by System-V-derived programs. They should have the same value if they're both set. The existence of both is an historical accident. (There could be cases where $USER is set and $LOGNAME isn't, but I don't know of any.)
The environ man page also documents a number of other common environment variables. (It doesn't document all environment variables because it would be impossible to do so.)
