Modus Operandi: Perps who obsessively leave riddles (or clues) at the scenes of their crimes. No one can ever figure these clues out except Batman (and anyone reading the comic who's more than 8 years old).
Real Life Villain: Rodney Alcala
Frankly, there've been a few infamous offenders who have adopted the Riddler's brilliant strategy - the most famous of which are Jack the Ripper and the Zodiac, who both sent multiple messages to the police daring them to catch them. Unlike their comic book counterparts, Jack and Zodiac were never caught, and they were more refined and brutal rather than silly and campy.
So instead of talking about them, let's talk about Rodney Alcala: the Dating Game Killer, so named because he won a televised game show in the middle of his horrendous spree. Yes, we're serious. Over the course of the show, he left numerous "riddles" and "clues." The choice quotes are: "The best time is at night... because that's the only time there is," and "I'm called the banana, and I look really good. Peel me!"
And in case that wasn't enough, the guy actually won the competition, but Cheryl Bradshaw (the bachelorette) refused to go on a date with him because he was too "creepy." The other contestants reported that he freaked people out, and at that point, he had already slain at least one person.