Hmmm I mean for best teams that *didn't* win a national title...
Kentucky in '16
UNLV in '91
Duke in '99
Illinois '89
That'd be my pick. And not in order, I mean there's a lot of 'order' you can go in.
Best teams of the last 30 years?
'90 UNLV
'92 Duke
'95 UCLA
'01 Duke
'04 UConn
Funny thing is I dunno - It's hard for me to put any UConn team in the top five generally speaking, but both '99 and '04 are a slam dunk for the top 10. '11 and '14 were good teams but they have blemishes on that kind of a resume. The '11 UConn team was every bit as good and a deserving National Champion... but they did fall off the cliff for 9 games. They just did. But I think they were a fantastic team that just kind of lost it for a spat. '14 was a team that just figured it out, but they weren't world beaters during the season.
Some other good ones out there to think about, too. Florida's back to back teams didn't suck. Arkansas was the first team I can honestly say I was scared of... they were soooooooo physical. Kentucky finally breaking through under Calipari... they were a good team, too.
The only ones I don't think there's much of any case for would be Syracuse in 03, I just didn't think much of them. I wasn't wild about UNC's '05 team. Arizona's '97 title winner was basically UConn in '14, who I'd have on the 'definiately no shot at the list' type of thing. Deserved it, figured it out, but no. Kentucky's '98 team was meh. I'm a tin foil hat wearer, but I still feel like something stunk when Duke beat UNLV in '91.
I'm all over the place now, but that's my initial thoughts...