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.
MAD once featured Dragged Net! (the radio/original tv version) and Dumbnet - A What IV Production (the 60s/70s version).