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IMHO, the best coach to ever coach at Ohio State was Paul Brown.  However, the best Ohio State coach was Woody Hayes.  

The difference is semantic, but major.  IMHO, Paul Brown was the best football coach ever, period.  He won Ohio State's first NC and also won Championships at the HS level (even more mythical than CFB) and in the NFL.  If not for WWII, he might have coached at Ohio State for 30 years (like Woody - 28) and if he had, he probably would have won a LOT of MNC's. I say that because he managed one, Ohio State's first, in just three years as HC.  Then he got drafted and coached Great Lakes Navy for the duration of WWII before coaching the Cleveland Browns to three NFL Championships in the 50's.  He had also won four HS NC's.  

When Ohio State reached #1 during the 1942 season, it was the first time they had ever achieved that.  Numerous Buckeye players drank bad water prior to the Wisconsin Game (in Madison) and the Buckeyes lost.  As I understand it, the team traveled on train cars that had been idled due to the war and were put back in service for the trip apparently with stagnant water in their tanks.  

Paul Brown can't be considered the best Ohio State coach because he was only 1-1-1 against Michigan, only won one NC, and never coached a bowl game.  

Woody Hayes has to be considered the best Ohio State coach because he won 13 league titles, 3-5 NC's (depends who you ask), went 205-61-10 overall, 152-37-7 in conference, 16-11-1 against Michigan, and won five bowl games including four Rose Bowls.

Paul Brown also endured a 3-6 1943 campaign as one of his three seasons; albeit due to several of the key players signing up for WWII.
Paul Brown's successor, Carrol C Widdows, deserves honorable mention.
In 1944 OSU was undefeated and untied; finishing 2nd in the National polls behind Army.
He followed that up with a 2-loss 1945 campaign, where both losses were to teams that finished in the top ten (Purdue and Michigan). 
In 1946, however, he made a cataclysmic mistake by switching titles with his offensive coordinator Paul Bixler, who proceeded to guide the team to a 4-3-2 outing that wound up getting both men canned at seasons end. 

Played in a weaker conference (I suspect Oklahoma, Colorado, and Kansas State fans might take exception to that)?

How'd you guess?  
Like most, Dr. Tom had trouble beating Barry, who toasted TO's Nebraska five straight one time, four straight another time, and just for good measure, three straight yet another.
But, and here's maybe the crucial but, TO did outlast Switzer and routed OU during our pathetic 90s, and ended up with a 13-13 mark all-time vs OU (we'd played twice one year, which is why there are 26 games against OU over his 25 seasons).  He even did something very un-Osborne-like and ran up the score in his last two games against OU.  Guess he was paying us back for all those hard years where OU knocked him out earlier in his career.

I do want to say as an opposing fan, there's no coach I admire more than Tom Osborne.  He's a class act.

I do want to say as an opposing fan, there's no coach I admire more than Tom Osborne.  He's a class act.

As a Husker fan, I have more respect and admiration for Doc Tom than any other football coach and most men I've met.

Stephen Orr Spurrier

122-27-1
.817 win% in 12 seasons
6 conference championships
1996 national championship

Meyer won 2 NCs, but SOS had a higher win% in twice as many seasons.  Florida coaches had topped out at a .686 win% (Ray Graves, Galen Hall) before Spurrier came back home in 1990.  Spurrier had it all, the ball plays, the swagger, the quips, and the visor.  He started at a program under probation and left it as a perennial top 5 program.  

So, Purdue... Well, it's a tough call between Ward Lambert [who coached John Wooden] and has the 1932 national title to his name, or Gene Keady. But I think Matt Painter has the potential to exceed Keady's heights, potentially starting with this year.

Oh, wait... You're talking about football??

In that case, I generally don't go back to the pre-WWII era, although that could give me a reason to claim Elmer Burnham and his stolen national championship. And yet another reason to hate Notre Dame.

In the modern era, it's gotta be Mollenkopf or Tiller. I'm going to give it to Mollenkopf because not only did he reach the Rose Bowl, he won it.

Tell us more! I have no idea about any of this except Tiller...

Well, here's the OU list of coaches:

http://soonerstats.com/football/coaches/ou/index.cfm#.Wl_k6UtG1Bw

We've got four to consider:

Benny Owen - who established a winning tradition at OU in the 1900s-20s
Bud Wilkinson - who established a national championship tradition at OU in the 1940s-60s
Barry Switzer - who reestablished a national championship tradition at OU in the 1970s-80s
Bob Stoops - who reinvigorated both the winning and national level presence at OU during the 2000s-10s

Bud and Barry won three national championships each.  Bob won one NC, but has the most wins of all.  All three had winning pcts of at least 80% and all three had 10 or more conference championships.  And all three had winning records against both Texas and Nebraska.  But Benny got the whole thing going.  I still think the stadium should be called Owen Field.  

So, who's best - you got me.

One worrisome thing about Lincoln Riley.  Unlike the four greats listed above, his first name does not start with the letter B.  Maybe he should change it to Blinkin' Riley ...

Hard to argue with a 12-2 first year though.

For the longest time, it was Owen Field at Oklahoma Memorial Stadium.  Now it's Owen Field at Gaylord Family/Oklahoma Memorial Stadium.
I say it's Bud Wilkinson.
Barry Switzer shades him on winning percentage and total wins, and Bob Stoops has him beat on total wins.  But Bud took a program that had fallen from Bennie Owen's 1905-1926 heights (which weren't all that high, winning 68% of the time) to Dewey Luster's 5-5 season in 1945 (and 27-18-3, 59%, overall).  And between Owen's departure and Luster's, OU had gone 3-13-1 against Texas.
Wilkinson arrived with Jim Tatum in 1946, and became HFC with Tatum's departure after an 8-3 season.  He went 145-29-4 in 17 seasons, with 14 Big 7/8 conference championships and 3 national championships.  He had winning streaks of 47 games and 31 games.
The knock on Bud is that the Big 7/8 was a weak conference and that, aside from Texas, which was not at a historic peak, and Notre Dame, he didn't play many good OOC games.  Bud went 9-2 vs. Texas in his first 11 seasons, but then lost his last 6 to finish at 9-8.  He went 6-2 in bowl games, mostly during the period when the Big 8 only allowed one team to go bowling, and did not allow the same team to appear in consecutive years.
Switzer--whose played in a tougher Big 8 conference--had a 157-29-4 record in 17 seasons.  He won 13 conference championships and 3 national championships, but he also lost 3 games in which a win would have given OU at least a split MNC.  He went 9-5-2 against Texas, and went 8-5 in bowl games.  Switzer inherited a good program from Chuck Fairbanks (77%, 3-1-1 in bowl games), so in that respect, his achievement is a little less impressive than Bud's.
But Switzer's personal behavior and his recruiting violations brought disrepute on OU, so I can't put him as our best coach ever.
Bob Stoops went 80% in a still tougher Big 12 conference in a period of CFB parity, went 9-6 against Texas, and he ran a pretty clean program by P5 standards, but his 9-9 bowl record, and 1-4 record in NC/CFP games put him a notch below Wilkinson and Switzer.

I'll put the Maryland candidate list out there and let MCWTERPS decide.

Jim Tatum
Jerry Claiborne
Bobby Ross
Ralph Friedgen