An article at bustle.com examines the question: how many U.S. serial killers were never caught? The piece is an interesting read, but ultimately it left me a bit unsatisfied simply because there is not enough data to support a truly good answer. Understandably, the author is forced to consider points such as: What's the technical definition of a serial killer? How many serial killers operate without ever being identified as serial killers? What impact do "low-profile" (my characterization) serial killers have on the question? etc. Though the article includes some well-sourced expert opinion, the final destination is, as I said, unsatisfying.
Not surprisingly, the author eventually mentions what is perhaps the most notorious unapprehended serial killer in United States history; of course, I'm referring to the Zodiac. First, there's an animated gif taken from David Fincher's 2007 film Zodiac in which Arthur Leigh Allen proclaims "I'm not the Zodiac" (an unanimated version is shown above). Shortly thereafter, the article continues:
More recently, the Zodiac Killer, who terrorized the Bay Area in the late '60s, also evaded capture, despite racking up at least seven confirmed victims (two of whom survived his attacks), being suspected in the deaths of several more people, and also sending his own taunting missives to the local press. As recently as this past January, people were still claiming to have clues to unmasking the Zodiac's identity, but nothing definitive has ever been proven.
From my perspective, it's more accurate to say that people are constantly claiming to have clues to unmasking the Zodiac's identity, for better or for worse (mostly for worse)...