Christian Laettner is well known for his last second jump shot on March 28, 1992 giving the Duke Blue Devils a 104-103 win over Kentucky in the East regional finals of the NCAA tournament. Duke went on to win the National Championship.
Indiana beat Kentucky on 12/10/2011 by the score of 73-72 on a last second, 3-point shot.
Gonzaga beat Kentucky in 1995-2007
The University of Kentucky has never been a 'recognized' national champion however they were selected as national champions in 1950 by the Sagarin Ratings and Bill Libby polls. They went 11-1 in 1950 under head coach Bear Bryant and defeated Oklahoma in the Sugar Bowl. Their only loss that season was to Tennessee who was named the national champion.
Kansas beat Kentucky 150 - 90
The Kentucky Wildcats last beat the Georgia Bulldogs in 2006, the score was 24-20.
Based on the date of this question, 11/17/14, Kentucky's schedule:On 11/14/14 Kentucky beat Grand Canyon 85 - 45On 11/16/14 Kentucky beat Buffalo 71 - 52Following the date of this question:On 11/23/14 Kentucky beat Montana State 86 - 28On 11/25/15 Kentucky beat Texas/Arlington 92 - 44All of these games were a part of the Cawood Ledford Classic between these five teams.
The gangs in Eastern Kentucky
Kentucky beat UNC Charlotte.
Villanova
beat
The most recent meeting I can find is December 15th, 2001 when Kentucky beat Kentucky State in men's basketball 118-63.
West Virginia beat Western Kentucky.