2015 UK and 2014 Wichita State are only 31-0 regular season teams in history

The top regular season win totals in UK history:
1) 31-0 (2015)
2) 30-1 (2012)
3) 29-2 (2010)
4) 27-2 (1948)
4) 27-4 (1997)
6) 26-1 (1996)
6) 26-3 (2003)
6) 26-3 (1986)
9) 25-0 (1954)
9) 25-1 (1949)
9) 25-1 (1970)
9) 25-2 (1978)

They aren't the first in NCAA Division I history to accomplish the 31-0 regular season mark, however.  That would be Wichita State, last year, which went 31-0 and finished 35-1 after falling to our Wildcats in the second round.

Examples I've found of 30+ win regular seasons:
1987 UNLV (30-1)
1998 Kansas (30-3)
2008 Memphis (30-1) (now vacated)
2014 Wichita State (31-0)

Most teams in the past played fewer regular season games.  So even the following teams that went undefeated didn't reach 31-0.

29-0 teams: 1975 Indiana, 1979 Indiana State
28-0 teams: 1968 Houston, 1976 Rutgers
27-0 teams: 1979 Alcorn State, 1991 UNLV, 2004 St. Joseph's

I will add to these lists as I research this further.  You'd be surprised by how inconsistent/inaccurate various sources can be.