REM or R.E.M. is an acronym for:

1. Rapid Eye Movement - a phase during sleep
2. R.E.M. - American rock music band formed in Athens, Georgia in 1980.
3. REM island - home of 1964 pirate Radio and TV Noordzee off the Dutch coastline.
4. REM programming language command - short for remark or reminder, used to preface a comment in both BASIC and DOS.
5. Roentgen equivalent man - a unit for measuring levels of exposure to radiation.
6. Rosicrucian Egyptian Museum