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All three of Northwestern's modern championships happened during years that they didn't have to play OSU, but beat Michigan.

History of Northwestern's League titles:
1903 co-championship shared with Michigan and Minnesota:
This is a weird one.  Apparently the conference back then treated ties as non-entities.  In the modern era ties were considered 1/2 a win.  Ie, the B1G's most recent ties were in 1995.  That year MSU finished 4-3-1 and the B1G Media guide reports that as a winning percentage of .563.  The math is MSU's wins (4.5) divided by MSU's games (8) to get 0.5625.  That was NOT the case in 1903.  Here are the top three teams in the conference standings in 1903:

• Michigan:  3-0-1, 1.000
• Minnesota:  3-0-1, 1.000
• Northwestern:  1-0-2, 1000

By the modern method, Michigan's and Northwestern's winning percentage would be 0.875 (3.5/4) while Northwestern's would be .667 (2/3).  However, back then ties were treated as if they didn't happen so all three teams were perfect in games not tied and shared the title.  

FWIW:  Northwestern beat Illinois by a point while tying Chicago and Wisconsin.  Minnesota and Michigan tied each other (6-6) and mauled their other opponents.  The six points given up in the tie with Minnesota were the only points that Michigan gave up all year.  Michigan finished 11-0-1 while outscoring their opponents 565-6.  Minnesota allowed six to Michigan and another six to Minneapolis Central High School while finishing 14-0-1 and outscoring their opponents 618-12.  
1926 co-championship shared with Michigan:
The Wildcats and Wolverines did not play each other and both finished 5-0.  The next best teams were Ohio State (3-1), Purdue (2-1-1), and Wisconsin (3-2-1).  Michigan played two of the three beating Ohio State by a point in Columbus and Wisconsin by 37 in Ann Arbor.  Northwestern played only one of the three, beating Purdue 17-0 in Evanston.  
1930 co-championship with Michigan:
Similar to 1926 in that the Wildcats and Wolverines did not play each other and both finished 5-0.  The only other team to finish above .500 in the league was Purdue (4-2) while Ohio State and Wisconsin both finished .500 at 2-2-1.  Michigan played two of the three beating Purdue by a point in Ann Arbor and Ohio State by 13 in Columbus.  Northwestern beat Ohio State by 17 in Evanston and Wisconsin by 13 in Evanston.  
1931 co-championship with Michigan and Purdue:
The three co-champions each finished 5-1 but Michigan did not play the other two.  In the only H2H among the co-champs, Northwestern lost to Purdue.  Purdue lost to Wisconsin and Michigan lost to Ohio State.  
1936 outright Championship:
Northwestern finished 6-0 ahead of Minnesota and Ohio State (both 4-1).  FWIW, the Wildcats beat both the Buckeyes (14-13 in Evanston) and the Gophers (6-0 in Evanston).  
1995 outright Championship:
Northwestern finished 8-0 ahead of Ohio State (7-1).  As @Brutus Buckeye mentioned, Northwestern did not play Ohio State.  The Buckeyes' loss was one of John Cooper's infuriating annual Michigan Meltdowns.  
1996 co-championship with Ohio State:
The Wildcats and Buckeyes did not play each other and both finished 7-1 ahead of Penn State and Iowa (both 6-2), Michigan and Michigan State (both 5-3).  Northwestern lost to Penn State (34-9) but beat Michigan (17-16) and Iowa (40-13).  The Wildcats missed Michigan State.  Ohio State lost to Michigan (13-9) in yet another of John Cooper's infuriating annual Michigan Meltdowns but beat Penn State (38-7) and Iowa (38-26).  The Buckeyes also missed Michigan State.  
2000 co-championship with Michigan and Purdue:
The Wildcats, Wolverines, and Boilermakers each finished 6-2 ahead of Ohio State (5-3).  No other team finished with a league record above .500.  Northwestern beat Michigan, lost to Purdue, and did not play Ohio State.  Their other loss was to Iowa.  The Boilermakers beat Northwestern and Michigan along with Ohio State but lost to Penn State and Michigan State.  The Wolverines lost to Purdue and Northwestern but beat Ohio State.  

Lake Forest was part of the initial meetings but decided to remain a small regional school rather than go B1G. Much of the Chicago brass wanted the same thing (minus the regional part), but Amos had a lot of pull back in those days. The brass eventually won out, and yes, MSU was the replacement for Chicago.

Note that Lake Forest was replaced by Michigan in between the initial discussions (which Michigan was not involved in) and the charter (by which time Michigan was in but Lake Forest was out).  
I've said this before, but IMHO, that was a HUMONGOUS difference.  The initial league but with Lake Forest instead of Michigan would have been essentially a Chicago-area conference:

• Northwestern:  Chicago-area small private school
• Chicago:  Chicago-area small private school
• Lake Forest:  Chicago-area small private school
• Illinois:  Large public school but in Chicago's state
• Wisconsin:  Large public school but not far from Chicago
• Purdue:  Large public school but not far from Chicago
• Minnesota:  Large public school 

I think that conference's most likely history would have involved expanding by bringing in other Chicago-area private schools and it would never have become a major national force.  Eventually the large public schools in that league (Illinois, Wisconsin, Purdue, Minnesota) would have left for greener pastures in whatever would have developed around the area.  

Replacing Lake Forest with Michigan gave the large public schools a supermajority of 5-2 in the initial membership which helped to lead to expansion including Iowa, Indiana, and Ohio State.  

Interesting history, merits its own thread perhaps.

there was once a poster who was posting interesting history information from the past 50 years or some such. but that idiot never finished and has lost most of the info since. still mad at myself for losing that.

if things slow down in the real world i might try and revive something similar that in the off season.

For all the talk about the Big 2 or Big 4 in the conference, OSU has pretty much owned this conference for a long, long time.  Especially since 2006.

There really is just a Big 1.

Who is #2 is debatable but there is no debate who is #1.

 i might try and revive something similar to that in the off season.

There's an off season?Since when?Who Knew?

https://www.youtube.com/watch?v=mw66ZZqzf7w

Twelving...

I figure after a decade or so, maybe 15 years, of mediocrity, any program starts to appear to be mediocre to younger folks.  I could see a recruit, for example, visiting Tenn or Michigan and thinking "I never knew they had so many trophies, and such a large stadium, and such nice facilities.".

They expect it at OSU and Alabama and Clemson.  The excitement in getting a letter from Tennessee might be somewhat dimmed.