The top teams of the six-round NCAA tournament era (and before)

Since 1985
1) Duke (4 titles, 12 FFs, 30 appearances)
2) UConn (4 titles, 5 FFs, 18 appearances)
3) North Carolina (3 titles, 9 FFs, 28 appearances)
4) Kentucky (3 titles, 8 FFs, 25 appearances)
5) Kansas (2 titles, 8 FFs, 30 appearances)
6) Florida (2 titles, 5 FFs, 17 appearances)
7) Louisville (2 titles, 4 FFs, 24 appearances)
8) Michigan State (1 title, 7 FFs, 25 appearances)
9) Arizona (1 title, 4 FFs, 27 appearances)
10) Syracuse (1 title, 4 FFs, 25 appearances)
11) UCLA (1 title, 4 FFs, 24 appearances)
12) Indiana (1 title, 3 FFs, 24 appearances)
13) Arkansas (1 title, 3 FFs, 18 appearances)
14) UNLV (1 title, 3 FFs, 15 appearances)

Missed the cutoff (fewer than 3 Final Fours):
Villanova, Michigan

Before 1985
1) UCLA (10 titles, 13 FFs, 22 appearances)
2) Kentucky (5 titles, 9 FFs, 29 appearances)
3) Indiana (4 titles, 5 FFs, 14 appearances)
4) North Carolina (2 titles, 9 FFs, 18 appearances)
5) Cincinnati (2 titles, 5 FFs, 10 appearances)
6) Oklahoma State (2 titles, 4 FFs, 9 appearances)
7) San Francisco (2 titles, 3 FFs, 14 appearances)
8) North Carolina State (2 titles, 3 FFs, 11 appearances)
9) Ohio State (1 title, 8 FFs, 13 appearances)
10) Louisville (1 title, 6 FFs, 17 appearances)
11) Kansas (1 title, 6 FFs, 14 appearances)
12) Utah (1 title, 3 FFs, 13 appearances)
13) Georgetown (1 title, 3 FFs, 9 appearances)
14) California (1 title, 3 FFs, 5 appearances)

Missed the cutoff (fewer than 3 Final Fours):
Marquette, Michigan State, UTEP, Loyola (Chicago), LaSalle, CCNY, Holy Cross, Wyoming, Stanford, Wisconsin, Oregon

Here are some detailed profiles of the top schools in the six-round era:

Duke
Current streak: made 20 in a row
Appearances: 30 (missed 1995)
Sweet 16s: 22
Elite 8s: 14
Final 4s: 12
Titles: 4

Appearances before 1985: 9
Sweet 16s before 1985: 6
Elite 8s before 1985: 6
Final 4s before 1985: 4
Titles before 1985: 0

Connecticut
Current streak: missed in 2015
Appearances: 18
Sweet 16s: 13
Elite 8s: 10
Final 4s: 5
Titles: 4

Appearances before 1985: 13
Sweet 16s before 1985: 3
Elite 8s before 1985: 1
Final 4s before 1985: 0
Titles before 1985: 0

North Carolina
Current streak: made 5 in a row
Appearances: 28 (missed 2002, 2003, 2010)
Sweet 16s: 20
Elite 8s: 15
Final 4s: 9
Titles: 3

Appearances before 1985: 18
Sweet 16s before 1985: 11
Elite 8s before 1985: 11 (2 during the 8-team era)
Final 4s before 1985: 9
Titles before 1985: 2

Kentucky
Current streak: made 2 in a row
Appearances: 25 (vacated 1988, missed 1989, 1990, 1991, 2009, 2013)
Sweet 16s: 18
Elite 8s: 15
Final 4s: 8
Titles: 3

Appearances before 1985: 29
Sweet 16s before 1985: 23
Elite 8s before 1985: 21 (4 during the 8-team era)
Final 4s before 1985: 9
Titles before 1985: 5

Kansas
Current streak: made 26 in a row
Appearances: 30 (missed in 1989)
Sweet 16s: 19
Elite 8s: 12
Final 4s: 8
Titles: 2

Appearances before 1985: 14
Sweet 16s before 1985: 9
Elite 8s before 1985: 9 (2 during the 8-team era)
Final 4s before 1985: 6
Titles before 1985: 1

Florida
Current streak: missed in 2015
Appearances: 17
Sweet 16s: 9
Elite 8s: 8
Final 4s: 5
Titles: 2

Appearances before 1985: 0
Sweet 16s before 1985: 0
Elite 8s before 1985: 0
Final 4s before 1985: 0
Titles before 1985: 0

Louisville
Current streak: made 9 in a row
Appearances: 24
Sweet 16s: 14
Elite 8s: 8
Final 4s: 4
Titles: 2

Appearances before 1985: 17
Sweet 16s before 1985: 14
Elite 8s before 1985: 6
Final 4s before 1985: 6
Titles before 1985: 1

Michigan State
Current streak: made 18 in a row
Appearances: 25 (missed 1987, 1988, 1989, 1993, 1996, 1997)
Sweet 16s: 15
Elite 8s: 9
Final 4s: 7
Titles: 1

Appearances before 1985: 4
Sweet 16s before 1985: 4
Elite 8s before 1985: 4
Final 4s before 1985: 2
Titles before 1985: 1

Arizona
Current streak: made 3 in a row
Appearances: 27 (vacated 1999 and 2008, missed 2010 and 2012)
Sweet 16s: 16
Elite 8s: 10
Final 4s: 4
Titles: 1

Appearances before 1985: 3
Sweet 16s before 1985: 2
Elite 8s before 1985: 1
Final 4s before 1985: 0
Titles before 1985: 0

Syracuse
Current streak: missed in 2015
Appearances: 25 (missed 1993, 1997, 2002, 2007, 2008, 2015)
Sweet 16s: 13
Elite 8s: 6
Final 4s: 4
Titles: 1

Appearances before 1985: 12
Sweet 16s before 1985: 8
Elite 8s before 1985: 3
Final 4s before 1985: 1
Titles before 1985: 0

UCLA
Current streak: made 3 in a row
Appearances: 24
Sweet 16s: 13
Elite 8s: 6
Final 4s: 4
Titles: 1

Appearances before 1985: 22
Sweet 16s before 1985: 19
Elite 8s before 1985: 15
Final 4s before 1985: 13
Titles before 1985: 10

Indiana
Current streak: 1
Appearances: 24
Sweet 16s: 9
Elite 8s: 4
Final 4s: 3
Titles: 1

Appearances before 1985: 14
Sweet 16s before 1985: 12
Elite 8s before 1985: 7 (1 during 8-team era)
Final 4s before 1985: 5
Titles before 1985: 4

Arkansas
Current streak: 1
Appearances: 18
Sweet 16s: 6
Elite 8s: 4
Final 4s: 3
Titles: 1

Appearances before 1985: 12
Sweet 16s before 1985: 4
Elite 8s before 1985: 6 (3 during 8-team era)
Final 4s before 1985: 3
Titles before 1985: 0

UNLV
Current streak: missed in 2015
Appearances: 15
Sweet 16s: 6
Elite 8s: 4
Final 4s: 3
Titles: 1

Appearances before 1985: 5
Sweet 16s before 1985: 4
Elite 8s before 1985: 1
Final 4s before 1985: 1
Titles before 1985: 0