The Flash isn't the only hero with a Rogues Gallery. Batman's got one, too, but his is different. The Flash rogues - Mirror Master, Captain Cold, Weather Wizard, etc. - are all bright and shiny in a 1950s science-fiction kind of way. Batman's villains, by way of contrast, are all much darker and sinister. In some measure, they're a product of their times, with film noir and pulp fiction providing substantial inspiration.
Two-Face is a representative villain this way, combining a tragic back-story with elements of 'Dr. Jeckyl and Mr. Hyde' into a memorable nemesis. Harvey Dent had been a prominent Gotham City District Attorney when a crime boss hurled a vial of acid at his face. Batman managed to deflect the vial only partially, so that it impacted on only one side of Dent's face, but even then the damage was severe. The acid severely mutilated the impacted side of Dent's face, but the psychological damage was even worse. Dent became obsessed with the duality of his appearance, and his behaviour soon changed to match.
Calling himself 'Two-Face', Dent became a master criminal, using a two-headed coin (with scratches carved into one side) to determine his actions in various circumstances. If the coin landed showing the clean side, then Two-Face would be merciful; if the scarred side showed, then there would be screaming, dying, and other assorted mayhem.
Mind you, Bats never had a hard time finding him. His targets always revolved around two themes over the years: duality, and the number two. You have to wonder what the property insurance rates must be for addresses in Gotham located on 2nd Avenue, Janus Street, and the like. Life insurance rates for twins (especially identical ones) must be especially high, too.
Isn't that just like a psychotic super-villain, to mess up the actuary tables so capriciously?