How many NCAA 1A football teams have completed an undefeated season since 1900?

Here is the list of all of the teams that have done it as of the end of the 2007-2008 year. 221 teams.

1900 Yale University 12-0-0
1900 Auburn University 4-0-0
1900 University of Texas 6-0-0
1900 Yale University 12-0-0
1901 University of Michigan 11-0-0
1901 University of Wisconsin-Madison 9-0-0
1901 Harvard University 12-0-0
1902 University of Michigan 11-0-0
1902 University of Nebraska 10-0-0
1903 Princeton University 11-0-0
1903 University of Nebraska 11-0-0
1904 University of Pittsburgh 10-0-0
1904 University of Pennsylvania 12-0-0
1904 University of Michigan 10-0-0
1904 University of Minnesota 13-0-0
1904 Vanderbilt University 9-0-0
1904 Auburn University 6-0-0
1905 University of Chicago 11-0-0
1905 Yale University 10-0-0
1906 University of Wisconsin-Madison 5-0-0
1907 Oregon State University 6-0-0
1908 Miami University (OH) 7-0-0
1908 Louisiana State University 10-0-0
1909 Yale University 10-0-0
1909 University of Arkansas 7-0-0
1909 University of Colorado 6-0-0
1909 University of Washington 7-0-0
1910 University of Pittsburgh 9-0-0
1910 University of Illinois 9-0-0
1910 Colorado College 7-0-0
1910 University of Colorado 6-0-0
1910 University of Washington 6-0-0
1911 University of Oklahoma 8-0-0
1911 University of Colorado 6-0-0
1911 University of Washington 7-0-0
1912 Harvard University
1912 University of Wisconsin-Madison 7-0-0
1912 Pennsylvania State University 8-0-0
1912 University of Washington 6-0-0
1913 Harvard University 9-0-0
1913 Auburn University 8-0-0
1913 University of Chicago 7-0-0
1913 University of Notre Dame 7-0-0
1913 University of Nebraska 8-0-0
1913 University of Washington 7-0-0
1914 Army 9-0-0
1914 University of Texas 8-0-0
1914 University of Illinois 7-0-0
1914 University of Tennessee 9-0-0
1914 Washington & Lee University 9-0-0
1915 Cornell University 9-0-0
1915 University of Oklahoma 10-0-0
1915 University of Nebraska 8-0-0
1915 University of Pittsburgh 8-0-0
1915 Colorado State University 7-0-0
1915 University of Washington 7-0-0
1916 University of Pittsburgh 8-0-0
1916 Army 9-0-0
1916 Ohio State University 7-0-0
1917 Georgia Tech 9-0-0
1917 University of Pittsburgh 10-0-0
1917 Ohio State University 8-0-1
1917 Texas A&M University 8-0-0
1917 Mare Island Marines 8-0-0
1917 University of Denver 8-0-0
1918 University of Oklahoma 6-0-0
1918 University of Texas 9-0-0
1918 University of Michigan 5-0-0
1918 Washington University (MO) 6-0-0
1918 Virginia Tech 7-0-0
1918 Presbyterian College 2-0-0
1918 Colorado School of Mines 4-0-0
1919 Centre College 9-0-0
1919 University of Notre Dame 9-0-0
1919 Texas A&M University 10-0-0
1920 University of Texas 9-0-0
1920 University of California 9-0-0
1920 VMI 9-0-0
1920 University of Notre Dame 9-0-0
1921 Cornell University 8-0-0
1921 University of Iowa 7-0-0
1921 Lafayette College 9-0-0
1921 Miami University (OH) 8-0-0
1922 Cornell University 8-0-0
1922 Princeton University 8-0-0
1922 University of Iowa 7-0-0
1922 University of California 9-0-0
1922 Drake University 7-0-0
1923 University of Illinois 8-0-0
1923 University of Michigan 8-0-0
1923 Yale University 8-0-0
1923 University of Colorado 9-0-0
1923 Cornell University 8-0-0
1923 Southern Methodist University 9-0-0
1924 University of Notre Dame 10-0-0
1925 University of Alabama 10-0-0
1925 Dartmouth College 8-0-0
1926 University of Utah 7-0-0
1928 Georgia Tech 10-0-0
1928 University of Detroit 9-0-0
1929 University of Notre Dame 9-0-0
1929 Purdue University 8-0-0
1929 Tulane University 9-0-0
1929 University of Utah 7-0-0
1930 University of Notre Dame 10-0-0
1930 University of Alabama 10-0-0
1930 University of Utah 8-0-0
1932 University of Southern California 10-0-0
1932 Colgate University 9-0-0
1932 University of Michigan 8-0-0
1933 Princeton University 9-0
1934 University of Minnesota 8-0-0
1934 University of Alabama 10-0-0
1935 Princeton University 9-0
1935 University of Minnesota 8-0-0
1938 Texas Christian University 11-0-0
1938 University of Tennessee 11-0-0
1939 Texas A&M University 11-0-0
1939 Cornell University 8-0-0
1940 University of Minnesota 8-0-0
1940 Stanford University 10-0-0
1940 Boston College 11-0-0
1940 Hardin-Simmons University 9-0-0
1940 Lafayette College 9-0-0
1941 University of Minnesota 8-0-0
1941 Duquesne University 8-0-0
1943 Purdue University 9-0-0
1943 USNTC Bainbridge 7-0-0
1943 Colorado College 7-0-0
1944 Army 9-0-0
1944 Ohio State University 9-0-0
1944 Randolph Field 12-0-0
1944 USNTC Bainbridge 9-0-0
1944 NAS Norman 9-0-0
1944 Fort Pierce 9-0-0
1945 Army 9-0-0
1945 University of Alabama 9-0-0
1945 Oklahoma State University 9-0-0
1946 University of Georgia 11-0-0
1946 University of Delaware 10-0-0
1947 University of Notre Dame 9-0-0
1947 University of Michigan 10-0-0
1948 University of Michigan 9-0-0
1948 Clemson University 11-0-0
1949 University of Notre Dame 10-0-0
1949 University of Oklahoma 11-0-0
1949 University of the Pacific 11-0-0
1950 Princeton University 9-0-0
1950 University of Wyoming 10-0-0
1951 Michigan State University 9-0-0
1951 University of Maryland 10-0-0
1951 Princeton University 9-0-0
1951 University of San Francisco 9-0-0
1952 Michigan State University 9-0-0
1954 Ohio State University 10-0-0
1954 UCLA 9-0-0
1954 University of Oklahoma 10-0-0
1955 University of Oklahoma 11-0-0
1955 Miami University (OH) 9-0-0
1956 University of Oklahoma 10-0-0
1957 Auburn University 10-0-0
1957 Arizona State University 10-0-0
1958 Louisiana State University 11-0-0
1959 Syracuse University 11-0-0
1960 Yale University 9-0-0
1960 New Mexico State University 11-0-0
1961 University of Alabama 11-0-0
1961 Rutgers University 9-0-0
1962 University of Southern California 11-0-0
1962 University of Mississippi 10-0-0
1963 University of Texas 11-0-0
1964 University of Arkansas 11-0-0
1966 University of Alabama 11-0-0
1966 San Diego State University 11-0-0
1968 Ohio State University 10-0-0
1968 Pennsylvania State University 11-0-0
1969 University of Texas 11-0-0
1969 Pennsylvania State University 11-0-0
1969 University of Toledo 11-0-0
1970 Arizona State University 11-0-0
1970 University of Toledo 12-0-0
1970 Dartmouth College 9-0-0
1971 University of Nebraska 13-0-0
1971 University of Toledo 12-0-0
1972 University of Southern California 12-0-0
1973 University of Notre Dame 11-0-0
1973 Pennsylvania State University 12-0-0
1973 Miami University 11-0-0
1974 University of Oklahoma 11-0-0
1975 Arizona State University 12-0-0
1975 Arkansas State University 11-0-0
1976 University of Pittsburgh 12-0-0
1976 Rutgers University 12-0-0
1979 University of Alabama 12-0-0
1980 University of Georgia 12-0-0
1981 Clemson University 12-0-0
1984 Brigham Young University 13-0-0
1986 Pennsylvania State University 12-0-0
1987 University of Miami (FL) 12-0-0
1988 University of Notre Dame 12-0-0
1991 University of Miami (FL) 12-0-0
1991 University of Washington 12-0-0
1992 University of Alabama 13-0-0
1993 Auburn University 11-0-0
1994 University of Nebraska 13-0-0
1994 Pennsylvania State University 12-0-0
1995 University of Nebraska 12-0-0
1997 University of Michigan 12-0
1997 University of Nebraska 13-0
1998 University of Tennessee 13-0
1998 Tulane University 12-0
1999 Florida State University 12-0
1999 Marshall University 13-0
2000 University of Oklahoma 13-0
2001 University of Miami (FL) 12-0
2002 Ohio State University 14-0
2004 University of Southern California 13-0
2004 Auburn University 13-0
2004 University of Utah 12-0
2005 University of Texas 13-0
2006 Boise State University 13-0


http://en.wikipedia.org/wiki/List_of_undefeated_Division_I_football_teams

12 teams have completed undefeated seasons with Indiana most recently in 1976. Hope this helps!