Was seldom presented so starkly by DC in the 1960s as with the Flash and the Reverse Flash. The Reverse Flash, also known as Professor Zoom, was a criminal from hundreds of years in the future who had stolen a Flash costume from a time capsule. By amplifying the super-speed wave patterns he found in the costume (don't laugh) Zoom was able to gain the speed power himself. The Flash managed to defeat him in Flash #139 (September 1963), but he was back a year later in Flash #147 for a terrific story called Our Enemy the Flash.
The story also featured the return of one of the Flash's earliest villains, Al Desmond, who had appeared in both Showcase #13 and #14, the last two tryout issues before Barry Allen was granted his own title. It is worth noting that Desmond appeared as two villains, both Mr Element and Dr Alchemy, in those issues. He was one of two DC characters I can think of who changed his supervillain identity in the Silver Age; the Signalman/Blue Bowman was the other.
But by Flash #147, Al Desmond was on the straight and narrow, and in this respect he was pretty unique in the DC universe, although of course Marvel had probably dozens of characters that started as villains and became heroes--the Scarlet Witch, the Black Widow, Hawkeye and Quicksilver to name just a few.
Professor Zoom, who lost his superspeed in the prior battle with the Flash, manages to hypnotize Desmond and forces him to bring him back to the past. He has discovered a metal called Element Z which allows him to travel at hypervelocity, but unfortunately it is unstable and thus he can only maintain the speed for awhile. So he naturally seeks out Mr Element for his chemical abilities.
And is dismayed to discover that Al's become a goody-two shoes. So he forces Desmond to commit a couple of crimes after which, improbably, Mr Element solves the problem of Element Z.
Professor Zoom heads back to the future leaving a despondent Mr Element behind. But the Flash, who suspects the truth behind Desmond's suddent lapse chases him on his cosmic treadmill. He defeats Zoom and returns to the past. Meanwhile Desmond has turned himself in along with the proceeds of his crime wave. Thanks to the Flash's explanation, Al is freed.
The Reverse Flash/Mr Element/Flash story continues in Flash #153's The Mightiest Punch of All Time. In this story, Professor Zoom is about to be freed from prison after being subjected to a "cerebro scanner" that reveals that he has been entirely rehabilitated. Not surprisingly, Zoom had managed to scam the scanner. He decides to resume his battle with the Flash by corrupting Al Desmond with a criminality-inducing ray.
The Reverse Flash manages to capture Barry. Desmond, realizing that he can only help as Mr Element, dons his costume and commits a crime. This gives Zoom an idea: Why not allow Mr Element to destroy the Flash? But the good side of Desmond wins out and he frees the Flash, who kayoes his evil counterpart. Flash then takes Al to the future, to undergo scientific rehabilitation. This time the cerebro scanner works properly and Desmond is finally free of his criminal past.