REM were one of the first popular rock bands in the late 80s and through the early 90s with assured albums such as 'Out of Time' in 1991 and 'Automatic For the People' in 1992 which were two of their most commercially successful albums.
Their later material arguably has not been able to attain the heights of these releases,although they have always remained a great live band,as was evident to me when I saw them in Manchester on their 'Around the Sun' European Tour in 2005.
They will be known for their many hits including the all conquering love song 'Everybody Hurts' the brilliant 'Losing My Religion', 'Nightswimming' 'Shiny Happy People' and 'Don't Go Back to Rockville' to name a few.
If you are unaccustomed to them best to check out 1991's 'Automatic For The People' and 92's 'Out of Time' or for a general idea check out the Best Of REM 1988-2003- In Time compilation.
I'm sure everyone has a favourite but as a reminder of how good a band they were,I have chosen 'Imitation of Life' from their 2001 Reveal album and what else but the ace 'Losing My Religion'.