An episode of It Takes a Thief (1968) titled "The Scorpio Drop" in which star Robert Wagner starts the Cold Open with "This is the city, Washington, DC. My name is Mundy...I'm a thief." Oddly enough on May 5, 2012 this episode aired on Digital station Antenna TV directly after an actual episode of Dragnet, without even a commercial between the Universal logo and the start of the parody.
An episode of The Monkees features Peter say, "Hey, its time for Dragnet! Anyone got a tv?" This shot is currently (May 2012) being used in an Antenna TV ad, which shows both programs in their line-up.
Seinfeld featured a character called Mr Bookman, a library official who behaved like Joe Friday. Another episode had Kramer channel a Joe Fridayish Inspector in order to get a stolen statue back from a cleaning man.
In L.A. Confidential, Jack Vincennes is the LAPD's advisor on the show "Badge Of Honour", which is clearly a DragnetExpy - one of the cast uses "Just the facts", with the implication that it's a recurring phrase in the show.
In the episode of The Simpsons entitled "Mother Simpson", Friday and Gannon investigate the return of Homer's long lost Mother, forced underground after a sixties protest incident. Harry Morgan voices Gannon.
A Looney Tunes Porky and Daffy cartoon called Rocket Squad is a straight-up parody, set IN SPACE! , where Daffy Duck plays "Sergeant Joe Monday". The twist is that the "Where Are They Now?" Epilogue shows him and his partner being arrested for wrongful arrest.