Did a little research and here's what I came up with. Looks like the 1980 Illinois game was the only game we've played versus a "Big Ten" team, although the Big Ten was previously called the "Western Conference".
Michigan
- Never Played
Michigan State
- 1947 lost 7-0 * Independent
- 1946 won 6-0 * Independent
- 1929 Lost 33-19 * Independent
- 1928 Tied 6-6 * Independent
Penn State
- Never Played
Illinois
- 1980 won 28-21
- 1923 lost 27-0 *Western Conference
Indiana
- 1932 lost 19-0 *Western Conference
- 1926 lost 19-6 *Western Conference
- 1920 Lost 24-0 *Western Conference
Purdue
- Never Played
Wisconsin
- Never Played
Northwestern
- Never Played
Ohio State
- Never Played
Iowa
- Never Played
Minnesota
- Never Played
Michigan
- Never Played
Michigan State
- 1947 lost 7-0 * Independent
- 1946 won 6-0 * Independent
- 1929 Lost 33-19 * Independent
- 1928 Tied 6-6 * Independent
Penn State
- Never Played
Illinois
- 1980 won 28-21
- 1923 lost 27-0 *Western Conference
Indiana
- 1932 lost 19-0 *Western Conference
- 1926 lost 19-6 *Western Conference
- 1920 Lost 24-0 *Western Conference
Purdue
- Never Played
Wisconsin
- Never Played
Northwestern
- Never Played
Ohio State
- Never Played
Iowa
- Never Played
Minnesota
- Never Played