These trophies are earned by winning the corresponding rivalry games:

Paul Bunyan's Axe: Minnesota vs. Wisconsin
Stanford Axe: Cal vs. Stanford
Apple Cup: Washington vs. Washington St.
Commonwealth Cup: Virginia vs. Virginia Tech
Golden Boot: Arkansas vs. LSU
Golden Egg Trophy: Mississippi St. vs. Ole Miss
Old Oaken Bucket: Indiana vs. Purdue
Victory Bell: UCLA vs. USC
Little Brown Jug: Michigan vs. Minnesota
Megaphone: Michigan St. vs. Notre Dame
Administaff Bayou Bucket: Houston vs. Rice
Marching Drum: Kansas vs. Missouri
Old Brass Spittoon: Indiana vs. Michigan St.
Territorrial Cup: Arizona vs. Arizona State
Silver Spade: New Mexico vs. New Mexico St.
Cy-Hawk Trophy: Iowa vs. Iowa St.
Sweet Sioux Tomahawk: Illinois vs. Northwestern
Ireland Trophy: Boston College vs. Notre Dame
Golden Hat: Oklahoma vs. Texas
Jeweled Shillelagh: Notre Dame vs. USC
Victory Bell: Cincinatti vs. Miami (OH)
Black Diamond Trophy: Virginia Tech vs. West Virginia