I'm talking genius level thinking that goes far beyond the pale. The protagonist of these shows demonstrates an analytical power that is supernatural, and they make it fun to follow the process.
1) House
(he's a jerk but he saves lives)
2) The Mentalist
He's a jerk too and quite often gets punched in the nose)
3) Sherlock Holmes (Brit or Rathbone or Cumberlink?)
(what can we say, he's the template, Jeremy Brit fan here though)
4) Elsbeth
(like Columbo but better and smarter and a fascinating character)
5) High Potential (not the UK version)
(Think Matt Damon in Good Will hunting, the protagonist even starts off as a janitor. It's fun watching her piece things together.)
6) Monk
When I had AI check my work, it made a compelling case for Monk. I never really watch the show but the sequel movie was great.
Honorable mention: Columbo, Pokerface. Psych and Lie to ME. The folks in these shows seem to have a superpower usually of observation but the super ability to come up with solutions based on a superior reasoning is not there like in my top 5.