as of 12/02/2010, Kansas has the longest current home winning streak at 64 games.
Current (prior to KU's win against UCLA as of this writing) can be found at http://web1.ncaa.org/stats/StatsSrv/rankings?sportCode=MBB&doWhat=showstreaks&division=1
For all-time streaks, here is a quasi answer, but Kentucky IMHO should have an asterisk as they have a history of being less than honorable during these years.
http://www.mikebond.org/2009/11/21/top-ten-ncaa-college-Basketball-home-winning-streaks/
Kentucky wildcats
Yes.
Syracuse
the uconn girls have an active streak of 89 games from 2008-present
The University of Kansas currently holds the record at 67 straight home wins. Go Jayhawks! I'm a proud Alumni
womens college basketball. uconn
UCLA has the longest overall winning streak. However the Butler Bulldogs have the longest CURRENT winning streak in men's division 1 college basketball. As of 3/26/2010 Butler has 23 consecutive wins.
Ucla
UCLA's 88 game win streak is the longest in mens basketball
Kentucky wildcats
There is no winning streak in the tournament as Ky the 2012 champion did not make the tournament this year.
As of Apr 18, 2013, Bryant University has the longest Division I Baseball winning streak, which is 19.
Uconn
Houston Rockets 22 winning streak
Kansas Jayhawks - 8 straight as of 2012 That's the current longest streak. Los Angeles City College holds the all time record at 14. UCLA holds the Div. 1 record at 13.
Wayland Baptist University 131 games during the 50's
57