During the Attitude Era, this became the primary way wrestlers would become top faces: if you were a really cool bad guy, you'd eventually have the crowd behind you enough that you became the de facto face.
Unfortunately, this had the side effect of turning practically everyone into a Draco in Leather Pants, to the point that that someone would have to be completely unacceptable (e.g., Jeff Jarrett) to avert this.
Mick Foley's disgust at wrestling fans in ECW led to him doing an inverted face heel turn (by ECW standards, the heels were faces) and he turned into an ECW "heel" (by other standards, this would be a face.) Indirectly, this had the same effect in the collapse of ECW as Hulk Hogan's for WCW.
On one hand, WWE barely averted this catastrophe as part of the fallout of the Montreal Screwjob. At the time, Bret Hart was the biggest star in WWE, and quite possibly one of the most popular wrestlers in history. At the time, this was taken almost as a white flag of surrender by Vince McMahon in the ratings war with WCW.
On the other hand, Vince made a startling discovery: you didn't need faces. The fans loved heels. From then on, the entire WWE was in a war of heels, led by Vince McMahon, Steve Austin, The Rock, Kurt Angle, and many more...It was the 90s.
It wasn't so much that it was nothing but heels battling out...that was WCW. The line simply shifted in a grayer direction as far as being a face. Austin, for instance, was a hero in the way John McClane is, meaning for all his positives, he's still a Badass asshole loner with a chip on his shoulder. It really just reflected the 90s as a whole.
The anti-heroes were also often the faces by comparison. Austin was a bit of a Jerkass but at least he wasn't abusing power at random (Vince McMahon) or subjecting innocent people to satanic sacrifices (The Undertaker).
And, of course, who can ever forget that the Screwjob was, to many, the unintentional birth of the "Mr. McMahon" character, who became synonymous with screwing over Austin's title chances in several creative ways.
During the infamous Invasion storyline, two entire companies (WCW and ECW) were portrayed as heels against the WWF/WWE. However, several of the wrestlers (Rob Van Dam in particular) were immensely entertaining and being cheered despite kayfabe trying to destroy the WWF. Almost immediately after the angle ended, Rob Van Dam, Stone Cold Steve Austin, the Hurricane, and Tommy Dreamer turned face once their quest to overthrow the WWF failed.
The very night after the angle ended, Austin was looking to wreak vengeance upon Kurt Angle for interfering in his fight with The Rock and costing the Alliance the victory. Despite the fact that Angle was saving the WWE, when Austin beat the crap out of Angle, the crowd erupted as if the last few months since Wrestlemania X-Seven never happened. The fans were just happy to have a Stone Cold they could cheer again. It was the most jarring, abrupt heel face turn in the history of prowrestling... and nobody had a problem with it.
Oddly enough, WWE heel Chris Jericho has been doing a nightly version of this — while still a heel on PPV and the other shows, on the rookie-oriented show NXT he becomes a Face in the eyes of Smarks whenever he joins Josh Matthews and Michael Cole on commentary, as he is sheer gold. He's also the "Pro" who's been most helpful to his rookie, Wade Barrett, and has gone out of his way on commentary to talk Barrett up, at one point demanding that Matthews and Cole do so too:
Jericho: Talk about Wade Barrett!
Josh Matthews: We are!
Mickie James was Trish Stratus's Stalker with a Crush and eventually turned heel on her...except the crowds cheered for her because they loved her Psycho Lesbian character. When Trish retired, Mickie became a face by default when hated heelLita cheated to win the title off her and sparked a feud. Even though her psycho characteristics were dropped she remained insanely popular for the rest of her career.
It's quite common in Professional Wrestling for heel wrestlers become popular for their movesets (especially common if the wrestler uses high flying moves, which are more associated with faces) and thus they have to turn face. Chris Jericho got this during his first Intercontinental Championship reign. Athena from SHIMMER is another example. As a result heels tend not to do too many flashy moves since they're not supposed to impress the crowd.
Depending on who you talk to, there could've been a brief turn for Vince Russo, who was a major heel in WCW, when he did his shoot promo at the Bash at the Beach 2000 event concerning Hulk Hogan. Even though there is constant debate on whether it was kayfabe or not (Russo was well known as a booker for "blurring the lines" between what was scripted and what was real life on any of the shows he booked), it's well known that Hulk Hogan's career has been marred by accusations of backstage politicking and using contract obligations to win matches that he shouldn't logically be able to win. This made many people relate to Russo's words (even though Russo himself was a very unpopular figure by that point).
Michael Cole seems to have gotten a unintentional turn (though he's since revealed that he was ready to go back to being face before this) due to how he handled himself on air during Jerry Lawler's Real Life heart attack during the September 10th 2012 episode of Raw. After the episode, fans have begun giving him more pops due to his professionalism and real emotion that he showed during the rest of that episode. Cole has not looked back since.
In a rare example of unscripted real-life events afftecting a wrestler's alignment, Darren Young was playing a heel in August 2013 when he spontaneously identified himself as gay to a TMZ reporter. Public reaction to Young's coming out was almost universally positive. On the episode of Raw three days later, he and his tag partner Titus O'Neill were booked as faces in a match against the Real Americans, received a massively positive crowd reaction, and have been treated as faces since then despite WWE's not having officially acknowledged Young's sexuality in-universe.
The Shield, a heel faction, started to turn face in the April/March of 2014 after having problems with Kane and the New Age Outlaws, and fully cemented their face status when Kane let it slip that Triple H had authorized an attack some weeks prior, and came to the aid of Daniel Bryan after a beatdown from Kane, Randy Orton, and Batista.