According to the NCAA FBS record book, the most-played rivalries are these (as of the beginning of this season):
126 Minnesota-Wisconsin
121 Miami (OH)-Cincinnati
121 North Carolina-Virginia
120 Missouri-Kansas
120 Georgia-Auburn
120 Oregon-Oregon St.
119 Purdue-Indiana
119 Stanford-California
118 Texas-Texas A&M
117 Navy-Army
117 Nebraska-Kansas
114 Clemson-South Carolina
114 Kansas-Kansas St.
113 Georgia-Georgia Tech
113 Michigan-Ohio St.
113 Mississippi-Mississippi St.
112 Utah-Utah St.
112 Tennessee-Kentucky
112 TCU-Baylor
111 Texas-Oklahoma
111 Oklahoma-Oklahoma St.
110 Tennessee-Vanderbilt
110 North Carolina St.-Wake Forest
108 Texas A&M-Baylor
108 North Carolina-Wake Forest
The list posted by Mick says Stanford and California have played 120 times, while the NCAA's list says 119 times. Both Stanford's and California's records agree with the NCAA's figure of 119 games, with this year being the 120th Big Game. Whoever compiled the 120 games on Mick's list may have got to 120 by adding the unofficial game in 1918, which neither Stanford nor California counts. Or maybe they counted this year already. . . .
126 Minnesota-Wisconsin
121 Miami (OH)-Cincinnati
121 North Carolina-Virginia
120 Missouri-Kansas
120 Georgia-Auburn
120 Oregon-Oregon St.
119 Purdue-Indiana
119 Stanford-California
118 Texas-Texas A&M
117 Navy-Army
117 Nebraska-Kansas
114 Clemson-South Carolina
114 Kansas-Kansas St.
113 Georgia-Georgia Tech
113 Michigan-Ohio St.
113 Mississippi-Mississippi St.
112 Utah-Utah St.
112 Tennessee-Kentucky
112 TCU-Baylor
111 Texas-Oklahoma
111 Oklahoma-Oklahoma St.
110 Tennessee-Vanderbilt
110 North Carolina St.-Wake Forest
108 Texas A&M-Baylor
108 North Carolina-Wake Forest
The list posted by Mick says Stanford and California have played 120 times, while the NCAA's list says 119 times. Both Stanford's and California's records agree with the NCAA's figure of 119 games, with this year being the 120th Big Game. Whoever compiled the 120 games on Mick's list may have got to 120 by adding the unofficial game in 1918, which neither Stanford nor California counts. Or maybe they counted this year already. . . .