It is generally accepted that our biggest rivals are up the road from Croydon. Prior to moving to The Amex, Portsmouth was marginally closer but Palace now have that honour, by 5 miles.
We have played Palace 107 times in competitive fixtures, dating back to Christmas day 1920. The stats have us on top (just):
Albion wins: 40
Palace wins: 38
Draws: 29
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. They include the numerous friendly meetings since WW2.
33/34 Div 3(S) - 24 Mar 34 (Home) W 4-1 The scan of this programme was very kindly provided by Peter Irvine of the Albion Collectors & Historians Society
47/48 Div 3(S) - 4 Oct 47 (Home) D 1-1
48/49 Div 3(S) - 16 Oct 48 (Away) W 2-0
49/50 Div 3(S) - 7 Jan 50 (Home D 0-0
50/51 Div 3(S) - 3 Feb 51 (Home) W 1-0
51/52 Div 3(S) - 26 Dec 51 (Home) W4-3
52/53 Div 3(S) - 23 Aug 52 (Home) W 4-1
53/54 Div 3(S) - 13 Mar 54 (Home) W3-0
54/55 Div 3(S) - 13 Nov 54 (Home) W 1-0
55/56 Div 3(S) - 14 Jan 56 (Home) W 5-0
56/57 Div 3(S) - 22 Apr 57 (Home) D 1-1
57/58 Div 3(S) - 23 Nov 57 (Away) W 4-2
57/58 Div 3(S) - 22 Mar 58 (Home) W 3-2
62/63 Div 2 - 1 Sep 62 (Away) D 2-2
62/63 Div 2 - 12 Jan 63 (Home) L 1-2
73/74 Friendly - 11 Aug 73 (Home) W 2-1
74/75 Div 3 - 17 Aug 74 (Home) W 1-0
74/75 Div 3 - 18 Mar 75 (Away) L 0-3
75/76 Div 3 - 23 Sep 75 (Away) W 1-0
75/76 Div 3 - 24 Feb 76 (Home) W 2-0
76/77 Div 3 - 2 Oct 76 (Home) D 1-1
76/77 FA Cup 1st Round - 20 Nov 76 (Home) D 2-2
76/77 FA Cup 1st Round Replay - 23 Nov 76 (Away) D1-1
76/77 FA Cup 1st Round 2nd Replay - 6 Dec 76 (Neut) L 0-1
76/77 Div 3 - 12 Mar 77 (Away) L1-3
77/78 Div 2 - 22 Oct 77 (Home) D 1-1
77/78 Div 2 - 18 Mar 78 (Away) D 0-0
78/79 Div 2 - 7 Oct 78 (Away) L 1-3
78/79 Div 2 - 17 Feb 79 (Home) D 0-0
79/80 Div 1 - 26 Dec 79 (Home) W 3-0
79/80 Div 1 - 5 Apr 80 (Away) D 1-1
80/81 Div 1 - 27 Dec 80 (Home) W 3-2
80/81 Div 1 - 18 Apr 81 (Away) W 3-0
81/82 Friendly - 14 Nov 81 Away D 1-1
82/83 Friendly - 7 Aug 82 (Away) L 0-1
83/84 Div 2 - 26 Dec 83 (Away) W 2-0
83/84 Div 2 - 21 Apr 84 (Home) W 3-1
84/85 Div 2 - 15 Sep 84 (Home) W 1-0
84/85 Div 2 - 2 Apr 85 (Away) D 1-1
85/86 Full Members Cup 1st Round - 18 Oct 85 (Away) W 3-1
85/86 Div 2 - I Jan 86 (Home) W 2-0
85/86 Div 2 - 29 Mar 86 (Away) L 0-1
86/87 Div 2 - 26 Dec 86 (Away) L 0-2
86/87 Div 2 - 20 Apr 87 (Home) W 2-0
88/89 Div 2 - 26 Dec 88 (Home) W 3-1
88/89 Div 2 - 27 Mar 89 (Away) L 1-2
92/93 Friendly - 7 Aug 92 (Home)
93/94 Friendly - 3 Aug 93 (Home)
95/96 Friendly - 2 Aug 95 (Home)
97/98 Friendly - 2 Aug 97 (Home)
02/03 Champ - 26 Oct 02 (Away) L 0-5
02/03 Champ - 25 Mar 03 (Home) D 0-0
05/06 Champ - 18 Oct 05 (Away) W 1-0
05/06 Champ - 20 Nov 05 (Home) L 2-3
11/12 Champ - 27 Sep 11 (Home) L 1-3
11/12 Champ - 31 Jan 12 (Away) D 1-1
12/13 Champ - 1 Dec 12 (Away) L 0-3
12/13 Champ - 17 Mar 13 (Home) W 3-0
12/13 Champ Play-off SF - 10 May 13 (Away) D 0-0
12/13 Champ Play-off SF - 13 May 13 (Home) L 0-2
17/18 Premier League - 28 Nov 17 (Home) D 0-0
17/18 FA Cup - 8 Jan 18 (Home) W 2-1
17/18 Premier League - 14 Apr 18 (Away) L 2-3
18/19 Premier League - 4 Dec 18 (Home) W 3-1
18/19 Premier League - 9 Mar 19 (Away) W 2-1
19/20 Premier League - 16 Dec 19 (Away) D 1-1
19/20 Premier League - 29 Feb 20 (Home) L 0-1
20/21 Premier League - 18 Oct 20 (Away) D 1-1
20/21 Premier League - 22 Feb 21 (Home) L 1-2