Depends what you define as mystery media.
To me, mystery media follows a kind of flow. An obstacle to be overcome like a puzzle, a whodunnit, whatdunnit, wheredunnit.
By that definition, supernatural would count. It follows that kind of pattern, every episode a new beasty pops up and the brothers have to find out what it is, what it wants, and how to kill it, it has a mystery as the central thread of every episode, and a larger mystery within each series.
Of course, there is stretching that definition too far. Stargate could be seen much the same, but I don't think so as it usually focuses more on the action than the solving of a mystery.
Another alternative mystery choice could be "House". Replace the killer with a killer condition, and you have your mystery, as House and his team race to find and cure the "killer".
As for my favourite, I'd have to say "Monk". I relate to the character's mannerisms and problems, I guess, although I'm not OCD, just very prone to nervousness.
Either that, or going back into my bending of the meaning of "mystery" series, "A town called eureka", possibly closer to sleuth stories than the other examples I discussed due to the fact that often, there is somebody behind the circumstances, and of course, the main character actually being a detective.
