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Per some stat I found, Illinois edges out Purdue, so that's what I went with. 

I’ll go with Temple.  Most wins without a title.  Chaney took them to five Elite 8’s between 88-01.  Never could get them to a FF though. Reached two FF in the 50s though.  

WVU could be on this list. Similar resume to most of the teams. 30 NCAA appearances, 2 FF, top 25 in wins. Literally came within one point in the 1959 title game.

I think if you add football and basketball wins WVU has the most without a championship in either sport. I won’t swear to it but I think that is correct.

My gut says Purdue, based on the list.  Awful lot of conference banners.

I went with Purdue myself - they have had lots of outstanding regular seasons, but for some reason or another, just couldn't finish the job in the tournament.

I'm not exactly surprised that Gonzaga isn't getting much love here - they're not in a P5 conference, nor have they ever been in a P5 or a P5-equivalent conference.  On top of that, they're definitely a Johnny-come-lately that had only modest success prior to the late 90s.  But they've been on an absolute tear the past decade or so, and have legitimately been able to go toe-to-toe with programs like Kentucky, UNC, Kansas, and the like and be at least competitive.

Most NCAA tourney wins without a title:

• t1. Oklahoma - 42 (t19th overall)
• t1. Purdue - 42 (t19th)
• 3. Illinois - 40 (23rd)
• 4. Notre Dame - 38 (t24th)
• 5. Kansas State - 37 (t28th)
• 6. Texas - 35 (t30th)
• t7. Gonzaga - 34 (t32nd)
• t7. Memphis - 34 (t32nd)
• 9. Temple - 33 (t34th)
• 10. West Virginia - 31 (36th)

Fewest NCAA tournament wins for a team with a title (aside from CCNY who is now D3)?  Holy Cross with 8.  Tournament only had 8 teams, and Holy Cross won 3 games to take the title in 1947.  They also won two games in 1948 (although one was a consolation game) and 1953.  They have lost 10 of their 11 games since beating Wake Forest in the 1953 Sweet Sixteen, with the lone win being a play in win for the 16 seed against Southern in 2016, before getting slammed by Oregon in the 1-16 game.  They did give a series of scares as a in a 2-15 against Kentucky in 2001, 1-17 against Kansas in 2002, 3-14 against Marquette in 2003, and 4-13 against Southern Illinois in 2007, but fell just short each time.

Looking forward to Purdue getting off this list.

Problem is that Purdue, as always, is perennially snakebit. 

Back in the Big Dog years we looked like monsters, and in 1994 as a 1 seed, due to a supposed injury from Big Dog wrestling another player while screwing around in the locker room (???) he hurt his back the night before the Elite Eight game and we missed the Final Four. 

2010 we had Hummel tear his ACL in a loss late in the season at Minnesota when we were I believe #3 in the nation and #1 and #2 lost that week. It was a monster team that had a shot at the title. Would have likely been a 1 seed with him healthy, and without him we dropped to a 4 seed but still made the Sweet Sixteen before losing to #1 seed Duke.

2011 we were coming into the season for Hummel's glorious return where he'd still be paired up with E'Twaun Moore and JaJuan Johnson for their final season and during the first day of practice (which was during the Purdue/Minnesota football game) it was reported he'd torn the ACL again. That team still played well and earned a 3 seed in the tourney, but it was the year of Virginia Commonwealth tearing through everyone on their way to the final four, and Purdue lost to VCU. 

2018 we were a 2 seed when Cal State Fullerton proved "the bigger they are, the harder they fall", dragging Isaac Haas to the ground and breaking his elbow. That team was a matchup nightmare for everyone, but without Haas--and particularly losing him IN the tournament, we only made the S16.

2019 we has Carsen go thermonuclear during the tournament, just lighting the world up [with a hell of an assist from Ryan Cline, particularly in the S16 game against Tennessee]. In the Elite Eight game we had the lead as the clock hit 00:00, but due to a CRAZY turn of events Virginia was able to get a circus shot off before the buzzer to tie, and Purdue lost in OT. 

F it man... After typing that, I need a goddamn drink. Ugh that it's only 8:21 AM :-(

Looking forward to Purdue getting off this list.

Problem is that Purdue, as always, is perennially snakebit.

Back in the Big Dog years we looked like monsters, and in 1994 as a 1 seed, due to a supposed injury from Big Dog wrestling another player while screwing around in the locker room (???) he hurt his back the night before the Elite Eight game and we missed the Final Four.

2010 we had Hummel tear his ACL in a loss late in the season at Minnesota when we were I believe #3 in the nation and #1 and #2 lost that week. It was a monster team that had a shot at the title. Would have likely been a 1 seed with him healthy, and without him we dropped to a 4 seed but still made the Sweet Sixteen before losing to #1 seed Duke.

2011 we were coming into the season for Hummel's glorious return where he'd still be paired up with E'Twaun Moore and JaJuan Johnson for their final season and during the first day of practice (which was during the Purdue/Minnesota football game) it was reported he'd torn the ACL again. That team still played well and earned a 3 seed in the tourney, but it was the year of Virginia Commonwealth tearing through everyone on their way to the final four, and Purdue lost to VCU.

2018 we were a 2 seed when Cal State Fullerton proved "the bigger they are, the harder they fall", dragging Isaac Haas to the ground and breaking his elbow. That team was a matchup nightmare for everyone, but without Haas--and particularly losing him IN the tournament, we only made the S16.

2019 we has Carsen go thermonuclear during the tournament, just lighting the world up [with a hell of an assist from Ryan Cline, particularly in the S16 game against Tennessee]. In the Elite Eight game we had the lead as the clock hit 00:00, but due to a CRAZY turn of events Virginia was able to get a circus shot off before the buzzer to tie, and Purdue lost in OT.

F it man... After typing that, I need a goddamn drink. Ugh that it's only 8:21 AM :-(

Lmao. I feel your pain.  That is a seriously bad run of luck.  The story about Robinson reminds me of a similar story I know of regarding WVU’s basketball team.

I know a dude who transferred in as an invited walk on back in the late 90s. One day after practice he and another player were horsing around in the locker room. The other guy put him in a figure four leglock and accidentally broke his leg, effectively ending his basketball career.