Since the Michigan-Ohio State game was moved to the final week of the conference season in 1935, the Wolverines and Buckeyes have decided the Big Ten championship between themselves 22 times. The following is a list of those classic match ups:

Wisconisin and
YEAR MOSURESULT
19441418 Ohio State is Big Ten champion. (Had UM won Michigan and Ohio State would have shared the title.)
194977 Michigan and Ohio State are co-champions; (OSU goes to the Rose Bowl because of a better overall record.)
195093 Michigan is Big Ten and Rose Bowl champion. (Had OSU won the Buckeyes would have won the title and Wisconsin would have gone to the Rose Bowl.)
1954721 Ohio State is Big Ten and Rose Bowl champion. (Had M won, the teams would have shared the title and M would have gone to the Rose Bowl.)
1955017 Ohio State is Big Ten champion but, by conference rules, cannot go to the Rose Bowl two consecutive years; Michigan State goes to Rose Bowl. (Had Michigan won, UM would won the title and gone to the Rose Bowl.)
1964100 Michigan is Big Ten and Rose Bowl champion. (Had OSU won, it would have been Big Ten champion.)
19681450 Ohio State is Big Ten and Rose Bowl champion. (Had UM won it would have won the title and gone to the Rose Bow.)
19692412 Michigan and Ohio State share the Big Ten championship and UM goes to the Rose Bowl. (Had OSU won it would have won the title outright.)
1970920 Ohio State is Big Ten champion and goes to the Rose Bowl. (Had UM won, it would have won the title.)
19721114 Michigan and Ohio State are co-champions, OSU goes to the Rose Bowl. (Had UM won it would have won the title outright.)
19731010 Michigan and Ohio State are co-champions; Athletic Directors' vote sends OSU to the Rose Bowl. (Winner of the game would have been Big Ten Champion.)
19741012Michigan and Ohio State are co-champions; Ohio State goes to Rose Bowl by beating Michigan. (Had UM won it would have won the title outright.)
19751421Ohio State is Big Ten champion and goes to the Rose Bowl. (Had UM won it would have won the title outright.)
1976220Michigan and Ohio State are co-champions; Michigan goes to the Rose Bowl by beating Ohio State. (Had OSU won it would have won the title outright.)
1977146Michigan and Ohio State are co-champions; Michigan goes to the Rose Bowl by beating Ohio State. (Had OSU won it would have won the title outright.)
1978143 Michigan and Michigan State are co-champions; Michigan goes to the Rose Bowl because MSU is banned from post-season play. (Had OSU won, Michigan State and Ohio State would have shared the title, sending OSU to the Rose Bowl.)
198093 Michigan is Big Ten and Rose Bowl champion. (Had OSU won, it would have won the Big Ten title outright.)
19862624 Michigan and Ohio State are co-champions; Michigan goes to the Rose Bowl by beating Ohio State. (Had OSU won, it would have won the title outright.)
19972014Michigan is Big Ten champion. (Had OSU won it would have shared the title with Michigan
20033521 Michigan is Big Ten champion. (Had OSU won, it would have won the title outright.)
2006 39 42 OSU is Big Ten champion. (Both teams were undefeated entering the game, OSU ranked #1 and UM #2 in national polls. UM finished tied for 2nd in Big Ten with Wisconsin. The Badgers did not play OSU.)
2007 3 14 OSU is Big Ten champion. (Both teams entered the game with one conference loss, each having lost the previous week. OSU won consecutive outright titles for the first time since 1954-55. UM finished in a tie for 2nd with Illinois.)
In addition, these 24 games had an effect in determining the Big Ten champion:
YEARMOSURESULT
1935 038Ohio State and Minnesota share Big Ten championship. (Had UM won, Minnesota would have won the title outright.)
1938180Minnesota is Big Ten champion (Had OSU won , it would have shared the title.)
1942721Ohio State is Big Ten champion (Had Michigan won, Wisconsin and Michigan would have shared title.)
1943457Michigan and Purdue are Big Ten co-champions. (Had OSU won, Purdue would have won the title outright.)
1948133Michigan is Big Ten champion. (Had OSU won, Michigan and Northwestern would have shared the title.)
1952727 Wisconsin and Purdue are Big Ten co-champions. (Had Michigan won, UM would have won the title outright.)
1956190 Iowa is Big Ten champion. (Had Ohio State won, OSU would have shared title.)
19612050 Ohio State is Big Ten champion. (Had Michigan won, Minnesota would have won title.)
19791518 Ohio State is Big Ten champion. (Had Michigan won, Ohio State, Purdue and U- M would have shared title.)
1981914 Ohio State and Iowa are Big Ten co-champions. (Had Michigan won, U-M would have won title.)
1984621 Ohio State is Big Ten champion. (Had Michigan won, Ohio State, Illinois and Purdue  would have shared title.)
19883431 Michigan is Big Ten champion. (Had OSU won, Michigan State and UM would have shared title.)
19892818 Michigan is Big Ten champion. (Had OSU won, Michigan, Illinois and Ohio State would have shared title.)
19901613 Michigan, Illinois, Iowa, and Michigan State are Big Ten co-champions (Had Ohio State won, OSU would have won the title outright.)
1991313Michigan is Big Ten champion (Had OSU won, Michigan would have shared the title with Iowa.)
1993280 Wisconsin and Ohio State are Big Ten co-champions. (Had OSU won, the Buckeyes would have gone to the Rose Bowl.)
19953123 Northwestern is Big Ten champion. (Michigan defeated previously unbeaten and second-ranked Ohio State. Had OSU won they would have shared the title and gone to the Rose Bowl.
1996 13 9 Ohio State and Northwestern are Big Ten co-champions. (Had OSU won, it would have won the title outright.)
19981631Michigan, Ohio State and Wisconsin are co-champions, Wisconsin goes to the Rose Bowl. (Had UM won it would have won the title outright and gone to a second straight Rose Bowl.)
20003826 Michigan, Purdue and Northwestern are Big Ten co- champions. (Had OSU won, it would have shared the title with Purdue and Northwestern.)
20012026 Illinois is Big Ten champion. (Had UM won it would have shared the title with Illinois and earned the conference berth into the Bowl championship Series.)
2002913Ohio State and Iowa tie for the Big Ten title. (Had UM won, Ohio and Michigan would have tied for second.)
20042137 Michigan and Iowa are Big Ten co-champions. (Had UM won it would have won the title outright. Had Wisconsin defeated Iowa the Badgers would have tied UM  for the title and gone to the Rose Bowl based on a better overall record.)
2005 2125 Ohio State and Penn State are co-champions.  (Had UM defeated OSU and Penn State lost to MSU, Michigan, Ohio State and Penn State would have tied for the conference title.)
2008 742 Ohio State and Penn State are co-champions.  (Had UM defeated OSU, Penn would have won the title outright.)
2009 1021 Ohio State is outright champion.  (Had UM defeated OSU, Penn State, Iowa and OSU would have tied for the title.)
2010 737 Ohio State clinches a tie for the Big Ten title with Wisconsin and Micihgan State at 7-1. BCS ratings determine who goes to the Bose Bowl.