I'd vote for Dr. Barry Mayfield - it seems like Columbo was genuinely ready to give up and only thought of the solution after he'd left the room!

Funny thing about that one though is all they had to do was plant someone beside Dr. Mayfield during the surgery with a court order that he had to hand over the suture that he removed immediately. They had a search warrant anyway. But then we wouldn’t have had the exciting ending in Dr. Mayfield’s office would we? 😀

Another thing about Mayfield, his intended victim lived. So he went through all that, including two completed murders, for nothing but to get Columbo off his back. His “almost getting away with it” always rang a little hollow for me.

In a way, one of them goes to both extremes, and that's Beth Chadwick.
She's about the only one to confess to the killing (though not as a murder) at the very beginning, but she's about the only one you see being cleared in a courtroom!
So I can't help liking it when she tells Columbo to stop coming to see her. She says it very "firmly," and you can hardly blame her.

I think there's two types of answer to this question. One we see on screen and one we can only speculate about.

I've often wondered how many of Columbo's cases would have collapsed in court.

In the case of Barry Mayfield for example, what would Mayfield's defence have made of the incriminating evidence turning up in Columbo's pocket?

Columbo was always good at finding means, motive and opportunity but in some cases you never actually see him prove that person carried out the murder.

Even though I'm one of its defenders, there's MIND OVER MAYHEM.
In spite of all the blunders Marshall Cahill makes, what makes him confess is Columbo arresting his son on a trumped-up charge (which he later ADMITS is a trumped-up charge), so why WOULD'T Marshall confess? (A little like Ned Diamond confessing to cover for Grace Wheeler, except that it's covering for someone who's actually innocent.) And according to Columbo, he probably couldn't get Marshall any other way, as in evidence.

Paul Hanlon comes to mind. He had Columbo stumped for awhile. The scene of Columbo sitting in the empty stands of the stadium is pretty iconic.