The show Dexter opens up an interesting yet controversial subject of saving innocent lives by eliminating potentially dangerous subjects (killer that kills other killers). Is this a complete novelty or have there been known cases of such killers in the past that might have inspired the show?
The TV show Dexter itself is based on the novel Darkly Dreaming Dexter by Jeff Lindsay.
There is a theory that the case of Manuel Pardo inspired the character, however, that is unconfirmed. He was an ex-cop and claimed he was "ridding the streets from the wicked" as a motive for his murders. There are not a lot of similarities between the character of Dexter and that case as far as I can see.
Jeff Lindsay himself, asked how he came up with the idea, jokingly (I assume...) answered
Watching a group of businessmen eat lunch. It occurred to me that serial murder wasn’t always a bad thing
And the question
Did you base Dexter on some known serial killer?
Got the answer of