It is generally accepted that our biggest rivals are from up the road in Croydon. Prior to the move to The Amex, Portsmouth was marginally closer but Palace now have that honour, by 5 miles.
Over the years we have played Palace 94 times in League and Cup and the stats have us on top (just):
Albion wins: 36
Palace wins: 34
Up until 1958, we were regular opponents in the old Division 3 (South) but into the 60s, our paths crossed less regularly.
As rivalries go, all was fairly quiet until a series of games in the mid 1970s that ignited passions on both sides! Much has been written about the development of the rivalry, which survives till this day.
Here are my programmes from our games (home and away) with Palace.
The Palace Rivalry
The scan of this programme was very kindly provided by Peter Irvine of the Albion Collectors & Historians Society