Together, they fight crime...and their sizzling, raging, off-the-wall, jealousy-fueled, Aw Look They Really Do Love Each Other UST.
A common trope of crime or cop shows, in which the two leads will have a tension that becomes a crux of the plot. It can apply to cops, medical examiners, helpful civilians, or anyone else who cleans up the streets for a living. Other exceptions include large ensemble casts of cops with regular hookups--the main definition of this one is when two people who are clearly the leads stretch it out for at least several seasons, and are the main ship of the series from the start.
Expect banter, even in a close-friend type situation, and thinly-hidden parallels to the couple in cases. Common obstacles to the big hookup might include one of them getting put in mortal danger, Girls of the Week related to the case, or just the rationalization of "our job is too dangerous for romance". To fuel the shipper's fire without solving anything, there might be a Fakeout Makeout along the way.
This trope can be done well and can...well, not. The first few seasons of the dance often go swimmingly, drawing additional viewers with the logic of "even if the case sucks, they'll still have a cute moment at some point!" But as with other UST, it's ending it that's the tricky part. Getting them together removes all that lovely viewer bait; stretching it out means they loose interest.
Straight: The X-Files, Moonlighting, Bones, Castle, Fringe
Aversions: Warehouse 13