I do not think UCLA had a national championship in 2001-02. UCLA had championships in spring of 2001 (2000-01 year) and fall of 2002 (2002-03 year), but I don't think they had any in the 2001-02 academic year. So I think UCLA's current championship streak is 13 years (2002-03 through 2014-15).
As Farm93 said, the next longest active streak is Penn State's 9 year streak.
So far as I can tell, the longest championship streaks ever are:
Stanford       39  1976-77 to 2014-15 (active)
U'S'CÂ Â Â Â Â Â Â Â Â Â 19Â Â 1959-60 to 1977-78
North Carolina   18  1980-81 to 1997-98
Arkansas       17  1983-84 to 1999-2000
UCLAÂ Â Â Â Â Â Â Â Â Â 13Â Â 1963-64 to 1975-76
UCLAÂ Â Â Â Â Â Â Â Â Â 13Â Â 1980-81 to 1992-93
UCLAÂ Â Â Â Â Â Â Â Â Â 13Â Â 2002-03 to 2014-15 (active)
LSUÂ Â Â Â Â Â Â Â Â Â Â 11Â Â 1986-87 to 1996-97
Denver        10  1959-60 to 1968-69
Yale           9   1904-05 to 1912-13
U'S'CÂ Â Â Â Â Â Â Â Â Â 9Â Â 1934-35 to 1942-43
Iowa           9  1977-78 to 1985-86
Texas          9  1982-83 to 1990-91
Penn State       9  2006-07 to 2014-15 (active)
Apologies if I missed something.
As Farm93 said, the next longest active streak is Penn State's 9 year streak.
So far as I can tell, the longest championship streaks ever are:
Stanford       39  1976-77 to 2014-15 (active)
U'S'CÂ Â Â Â Â Â Â Â Â Â 19Â Â 1959-60 to 1977-78
North Carolina   18  1980-81 to 1997-98
Arkansas       17  1983-84 to 1999-2000
UCLAÂ Â Â Â Â Â Â Â Â Â 13Â Â 1963-64 to 1975-76
UCLAÂ Â Â Â Â Â Â Â Â Â 13Â Â 1980-81 to 1992-93
UCLAÂ Â Â Â Â Â Â Â Â Â 13Â Â 2002-03 to 2014-15 (active)
LSUÂ Â Â Â Â Â Â Â Â Â Â 11Â Â 1986-87 to 1996-97
Denver        10  1959-60 to 1968-69
Yale           9   1904-05 to 1912-13
U'S'CÂ Â Â Â Â Â Â Â Â Â 9Â Â 1934-35 to 1942-43
Iowa           9  1977-78 to 1985-86
Texas          9  1982-83 to 1990-91
Penn State       9  2006-07 to 2014-15 (active)
Apologies if I missed something.
