Law & Order: Lennie Briscoe and Mike Logan
The original Law & Order went through several partners for Chris Noth's Mike Logan before hitting on this successful duo. Briscoe always had a wisecrack to make about the case or the suspects, while Logan was a hothead that needed to be reeled in from time to time. Together, they were so memorable that many viewers consider the late Jerry Orbach to be the face of the show even though he didn't appear until the third season.
Law & Order: SVU: Olivia Benson and Elliot Stabler
1999 saw television give birth to a new Law & Order series that dealt with sex crimes instead of murders and allowed the lead cops to have more personal, human stories. For the next 12 years, the chemistry sizzled as Olivia Benson and Elliot Stabler tried their best to solve cases without letting the horrors they saw get to them. Their partnership never went beyond friendship, but the heat between them was so high that Stabler's wife was sometimes jealous, and ever since Christopher Meloni's departure in 2012 many fans have been hoping for a reunion.
Monk: Adrian Monk and Sharona Fleming
While technically not a cop partnership (he was a consultant for the local police with crippling OCD and she was his live-in nurse), Adrian Monk and Sharona Fleming were nevertheless an endearing crime-fighting duo. Sharona was gruff and took no nonsense, and she helped balance out Monk's OCD qualities so that he was able to use his attention to detail to solve crimes rather than to get distracted by minutia.
Bones: Seeley Booth and Temprance Brennan
This mystery-solving partnership between an FBI detective with a gambling problem and a forensic anthropologist who most likely had Aspergers' Syndrome was the heart and soul of the long-running procedural Bones. They gelled together so well that they eventually married, which says a lot for the strength of their partnership (and the idea that opposites attract.)
The Mentalist: Patrick Jane and Teresa Lisbon
The Mentalist's Patrick Jane was a unique type of detective: a con artist who used his knowledge of how to pull the wool over people's eyes to figure out who was lying and to trick suspects into confessions. His unconventional methods were balanced out by partner Teresa Lisbon's more traditional detective training, and the two became one of the most fascinating cop partnerships in history.
Rizolli & Isles: Jane Rizolli and Maura Isles
Wisecracking Jane Rizzoli couldn't have found a better partner than her forensic-knowledge-obsessed, literal minded best friend Maura Isles. For six years, the two made the Boston PD Homicide Division an entertaining, exciting place to work and their banter and friendship will be missed for years to come.