I just realized that with The Beatles' White Album surpassing Van Morrison's Astral Weeks in the last update as the #1 album of 1968, the Beatles' tally of #1 albums comes to 3:

1964 - A Hard Day's Night
1968 - The Beatles
1969 - Abbey Road

That means they are tied with Radiohead for the most #1's:

1997 - OK Computer
2000 - Kid A
2007 - In Rainbows

Also worth noting, the Beatles still have three (!) #2 albums: Rubber Soul ('65), Revolver ('66), and Sgt. Pepper ('67), and Radiohead also has a #2 album in The Bends ('95). Aside from Rubber Soul, all of those albums rank very close to the #1 albums of their respective years.