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 "writers' poll" by Associated Press (AP) was the most popular, followed by the "coaches' poll" by United Press International) (UPI). Prior to 1965, both services issued their final polls at the close of the regular season, but before teams competed in bowl games. For the 1965 season, the AP took its final poll after the postseason games, an arrangement made permanent in 1968. The Associated Press presented the "AP Trophy" to the winner.
The AP poll in 1965 consisted of the votes of 55 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. In the preseason poll for 1965, the writers cast first place votes for 9 different teams, and the range of points between the highest six finishers ranged from 252 to 311 points. Nebraska was #1 in the preseason rankings, followed by 2.Texas 3.Notre Dame 4.Michigan 5.Alabama 6.Arkansas.^[3] As the regular season progressed, a new poll would be issued on the Monday following the weekend's games.
At season's end, Michigan State, Arkansas and Nebraska were all unbeaten, with records of 10-0-0, and as champions of the Big Ten, Southwestern and Big 8 conferences, respectively, they played in three separate bowl games (Rose, Cotton and Orange). Arkansas and Michigan State lost in their bowl games, and Alabama defeated Nebraska in the Orange Bowl. In the poll taken after the bowls, Alabama was crowned the national champion by the Associated Press. The school had been #1 in the UPI coaches' poll at the end of the 1964 season. Taken from http://en.wikipedia.org/wiki/1965_college_football_season.

Final Stats:

Rank	Team	Coach	Top QB	Top RB	Top WR	Top NFL Player
1	Alabama	Bear Bryant	Steve Sloan	Steve Bowman	Tommy Tolleson	WR Ray Perkins picked 110th by BAL
2	Michigan State	Duffy Daugherty	Steve Juday	Clinton Jones	Gene Washington
3	Arkansas	Frank Broyles	Jon Brittenum	Bobby Burnett	Bobby Crockett	T Dick Cunningham picked 136th by DET
4	UCLA	Tommy Prothro	Gary Beban	Mel Farr	Kurt Altenberg	WR Dick Witcher picked 119th by SFO
5	Nebraska	Bob Devaney	Fred Duda	Harry Wilson	Freeman White	DT Walt Barnes picked 21st by WAS
6	Missouri	Dan Devine	Gary Lane	Charlie Brown	Monroe Phelps	G Bruce Van Dyke picked 174th by PHI
7	Tennessee	Doug Dickey	Dewey Warren	Walter Chadwick	Johnny Mills	LB Frank Emanuel picked 52nd by PHI
8	Louisiana State	Charles McClendon	Nelson Stokley	Joe Labruzzo	Doug Moreau	DT George Rice picked 12th by CHI
9	Notre Dame	Ara Parseghian	Bill Zloch	Nick Eddy	Nick Eddy	DE Pete Duranko picked 61st by CLE
10	Southern California	John McKay	Troy Winslow	Mike Garrett	Dave Moton	RB Mike Garrett picked 18th by RAM