After seeing a preview for “Sleepy Hollow”, it occurred to me that maybe we’ve exhausted the possibilities of this genre. I mean, “Sleepy Hollow”'s theme is “she’s a cop, he’s a 250 year old undead Revolutionary War spy!” Um…what? Then we have “Almost Human”, which steals their premise from Joey Tribiani.
There’s plenty out there - what else do we have? Can we encourage TV execs to move on to the next idea, please?
Ah, the Wunza. “Wunza XXXX from YYYY with a penchant for ZZZZ. The other is a QQQQ MMMMM who likes to NNNNN. Together they fight crime.”
Eleventeen Jillion.
Oy.
I watch my share - currently giving Elementary a shot - but yeah, it is a formula whose overuse boggles the mind.
I was going to link to the TV Tropes page for that, but it’s surprisingly sparse.
30 Rock had the ultimate version of this with GOD COP.
“I think Esposito lied to us.”
“What do you mean you think? You’re GOD! I don’t understand the rules of this.”
“Let us pray.”
“TO WHOM?”
I haven’t watched it in a couple of seasons, but *Castle *appears to fit the bill – she’s a tough NYPD cop from homicide, he’s a mystery novelist.
This might be out of the strict meaning of the trope:
Rizzoli and Isles: One’s a cop, the other’s a medical examiner.
Come for the police procedural, stay for the lesbian subtext. 
Lie to Me is cancelled, I think. A cop and a guy who could tell you were lying. The Mentalist-- a cop and a guy who cold reads.
Just to have mentioned them and to admit to liking them anyway, how about:
ETA: Hi, Biggirl
Psych
You gotta say what the ridiculous pairing is. Of these, Elementary is one of my favorites:
Elementary: private detective (of sorts) + sober life companion!
That’s more of a buddy cop pairing, since neither are LEOs - but it’s certainly of the same “arguably qualified person and their sidekick” formula. Gus certainly brings something to the table during investigations, but usually pretty rarely.
The only reason I ever watch it is for the lasbian subtext. As a cop show, it sucks.
On a technicality, there’s Agents of SHIELD, where the investigation-and-enforcement types who answer to the Deputy Director would be lost without the useful contacts and computer savvy of their new civilian consultant.