During the 20th century, the NCAA had no playoff for the college football teams that would later be described as "Division I-A". The NCAA did recognize a national champion based upon the final results of "wire service" (AP and UPI) polls. The extent of that recognition came in the form of acknowledgment in the annual 'NCAA Football Guide of the "unofficial" national champions. The AP poll in 1961 consisted of the votes of 45 sportswriters, each of whom would give their opinion of the ten best teams. Under a point system of 10 points for first place, 9 for second, etc., the "overall" ranking was determined. Although the rankings were based on the collective opinion of the representative sportswriters, the teams that remained "unbeaten and untied" were generally ranked higher than those that had not. A defeat, even against a strong opponent, tended to cause a team to drop in the rankings, and a team with two or more defeats was unlikely to remain in the Top 10. The top teams played on New Year's Day in the four major postseason bowl games: the Rose Bowl (near Los Angeles at Pasadena), the Sugar Bowl (New Orleans, Louisiana), the Orange Bowl (Miami, Florida), and the Cotton Bowl (Dallas, Texas). Taken from http://en.wikipedia.org/wiki/1961_college_football_season.

Final Stats:

Rank	Team	Coach	Top NFL Player
1	Alabama	Bear Bryant	G Billy Neighbors picked 43rd by WAS
2	Ohio State	Woody Hayes	LB Sam Tidmore picked 81st by CLE
3	Texas	Darrell Royal	HB Jimmy Saxton picked 146th by STL
4	Louisiana State	Paul Dietzel	LB Roy Winston picked 45th by MIN
5	Mississippi	John Vaught	G Bookie Bolin picked 58th by NYG
6	Minnesota	Murray Warmath	WR Tom Hall picked 94th by DET
7	Colorado	Everett Grandelius	LB Jerry Hillebrand picked 13th by NYG
8	Michigan State	Duffy Daugherty	FL Gary Ballman picked 104th by PIT
9	Arkansas	Frank Broyles	FL Lance Alworth picked 8th by SFO
10	Utah State	John Ralston	DT Merlin Olsen picked 3rd by RAM
11	Missouri	Dan Devine	G Ed Blaine picked 28th by GNB
12	Purdue	Jack Mollenkopf	G Larry Bowie picked 73rd by MIN
13	Georgia Tech	Bobby Dodd
14	Syracuse	Ben Schwartzwalder
15	Rutgers	John Bateman
16	UCLA	Bill Barnes	LB Andy Von Sonn picked 189th by CHI
17	Arizona	Jim LaRue	DB Bobby Thompson picked 38th by DET
18	Penn State	Rip Engle	LB Bill Saul picked 23rd by BAL
19	Rice	Jess Neely	WR John Burrell picked 92nd by SFO
20	Duke	Bill Murray