always a fun topic and it depends on the objective and subjective criteria that each analyst uses and how they value those criteria.
If it is all about championships...then UCLA trumps all but it can't just be about championships as that makes for a short and boring discussion and most of us agree the tourney, while a blast, is kind of a horrible way to pick a champion. I think you need to look at different criteria and I also believe that more recent results should get weighted more heavily, at least i none or two categories. I attempted to compile a list, I think in 2006 and the categories I used were somewhat dependent on information I could fine somewhat easily on the internet. As I recall they were something like this: all time wins, all time win %, win % since 1990 (gave some recency bias and someone had compiled the data), Final Fours, National Championships (in the ff & NC categories I double weighted each that occurred after expansion to 64). I also had ave. ncaa seed since 1985 to try to reward what others thought were great regular seasons and that really dinged teams that had missed the tourney. I did not want to use conference titles as I thought that would be a KU bias.
Now a LOT has happened since mid season 2006 and UNC in particular would move up but this was the top 15 using those criteria at that time:
Kentucky
Duke
Kansas
North Carolina
UCLA
Syracuse
Indiana
Arizona
Cinci
Illinois
utah
louisville
uconn
arkansas
temple
My current all time list would be:
Kentucky
UNC
Kansas
Duke (really coin flip with KU, KU got the homer nod)
UCLA
Indiana
If listing who I think the top/biggest programs are right now...kind of a more subjective, who has the juice from the public, media, recruits I would probably go:
Duke
UNC
Kentucky
Kansas