The 1983 NCAA Division I-A football season ended with the University of Miami, led by Bernie Kosar, winning their first national championship over perennial power and top ranked Nebraska in the Orange Bowl.
The 31-30 win over Nebraska is still talked about as one of the greatest games of all time, not only for its last minute finish, but for its role in changing the face of college football. Miami came into the game ranked #5, but losses by #2 Texas in the Cotton Bowl and #4 Illinois in the Rose Bowl launched them to #1 (despite protests from #3 Auburn)
Nebraska scored a touchdown with 48 seconds remaining, putting them within one point of the Hurricanes. Despite knowing a tie would still give Nebraska the national title, Coach Tom Osborne decided to go for two points and the win rather than one point and the tie. Miami was able to hold, snapping Nebraska's 22-game winning streak and launching Miami as a powerhouse program.
This Miami team was the first to win a national title without a single player voted to the first team All-Americans and only the second to win a national title gaining more passing yards than rushing.
The Auburn Tigers, featuring Bo Jackson also had a stellar season going 11-1 and beating Michigan in the Sugar Bowl 9-7. Despite entering the bowl games ranked third in both major polls, and with both teams ranked higher losing their bowl games, the Tigers ended ranked third in the final AP poll as Miami jumped from 5th to ranked #1 when they beat #1 ranked Nebraska to gain the National Championship.^[2] Auburn had played the toughest schedule in the nation, including eight bowl teams, seven of which were ranked in the top 20 (four in the top ten). Even with this difficult schedule the Tigers were ranked first by a few polls, including the New York Times computer rankings. The NCAA record book also formally recognizes the Tigers as co-national champions, along with Nebraska (and of course, Miami). ^[3] It is not uncommon for the NCAA record book to "recognize" multiple national champions in a given year, with the AP and Coaches' poll winner regarded as true national champions.
The Holiday Bowl was also a classic, as BYU, led by future NFL star Steve Young, defeated Missouri with a last second halfback pass.
The annual rivalry game between Oregon and Oregon State is still widely known and derided as "The Toilet Bowl", as the teams played to a 0-0 tie, the last scoreless tie in college football. The game featured 11 total turnovers, as 6 fumbles were lost (out of 11 total), 5 interceptions, and 4 missed field goals.
This season saw no conference have two or more teams tie for the title—an event that did not happen again in either Division I-A or its successor, Division I FBS, until 2009. (Note, however, that even when a conference officially recognizes multiple champions, it will invariably have some kind of tiebreaker system to determine placement for bowl berths.)
Due to the school's financial troubles the NCAA demoted North Texas to Division 1-AA for the 1983 season dropping the number of Division 1-A teams to 112 (North Texas would later move back up to Division 1-A in 1995). Taken from http://en.wikipedia.org/wiki/1983_NCAA_Division_I-A_football_season.

Final Stats:

Rank	Team	Coach	Top NFL Player
1	Miami (FL)	Howard Schnellenberger	RB Keith Griffin
2	Nebraska	Tom Osborne	WR Irving Fryar
3	Auburn	Pat Dye	NT Doug Smith
4	Georgia	Vince Dooley	G Guy McIntyre
5	Texas	Fred Akers	G Doug Dawson
6	Florida	Charley Pell	LB Wilber Marshall
7	Brigham Young	LaVell Edwards	LB Todd Shell
8	Michigan	Bo Schembechler	DB Evan Cooper
9	Ohio State	Earle Bruce	G William Roberts
10	Illinois	Mike White	LB Ed Brady
11	Clemson	Danny Ford	DB Rod McSwain
12	Southern Methodist	Bobby Collins	NT Michael Carter
13	Air Force	Ken Hatfield
14	Iowa	Hayden Fry	T John Alt
15	Alabama	Ray Perkins	RB Joe Carter
16	West Virginia	Don Nehlen	QB Jeff Hostetler
17	UCLA	Terry Donahue	QB Jay Schroeder
18	Pittsburgh	Foge Fazio	C Jim Sweeney
19	Boston College	Jack Bicknell	WR Brian Brennan
20	East Carolina	Ed Emory	RB Earnest Byner