Bret Hart vs. Stone Cold, WrestleMania 13. The end of the match had Hart putting on the Sharpshooter on Austin, and Austin is bloodied and desperately crawling to the ring ropes and passes out in a pool of his own blood. That iconic image would be the start of Austin's Wrestlemania moments of glory.
The fans' support for Stone Cold's refusal to tap to the Sharpshooter, despite being a heel, is what would more or less jumpstart his turn to fan favorite and resident badass of the WWF.
There's a moment when Austin begins to pull himself up as if he is going to break the Sharpshooter, and the blood really starts to pour down. The fan response is chilling.
A standout moment: Austin finally gets to wrestle Vince, in a steel cage no less, at St. Valentine's Day Massacre in 1999. It quickly turns into Stone Cold kicking Vince's assall over the arena. At one point, Vince is flung from the top of the cage through the Spanish Announce Table, and when Howard Finkel attempts to announce Austin as the winner by forfeit, Austin rightfully points out that the match hadn't actually started yet. Rarely is that level of sadism so awesome.
Austin: Now, jackass! Jackass, that's you in the black! Is the son of a bitch still breathing? Well, since he is still breathing, if you want me to finish this can of whoop-ass, gimme a hell yeah!
Any time he gets behind the wheel (a monster truck, beer truck, The Rock's Cadillac, cement mixer) one can expect this. The most awesome is regarded as when he drove a Zamboni up to the ring in Detroit so he can fly over the cops protecting Vince McMahon.
A moment that may rival the awesomeness is the beer truck. Austin drives a beer truck to the ring, and cuts a fantastic promo on the Rock whilestanding on top of the beer truck.
Austin: For the last few weeks, I come out here, and I sit here and listen to you spin your little nursery rhymes about "Jabroni Avenue" or "Know Your Role Boulevard"; Jesus Christ, son, you better get your ass serious, because Stone Cold Steve Austin is gonna take his ass to Philadelphia, check right in to the Smackdown Hotel, roll right in to room 3:16, and burn that son of a bitchTO THE GROUND!
Then, to cap it all off, he gets a hose from the beer truck and floods the Corporation with beer. The crowd was going crazy.
His even greater Big Damn Heroes moment, Stone Cold returning to his old self in 2001, saving Team WWF from the Alliance, entering to a truly massive pop with Conservation of Ninjutsu in full effect. Check it out here
But the best ever Big Damn Heroes moment? Showing up on Raw after a brief absence, to help Mick Foley win his first title over The Rock, and in the process receiving, quite possibly, the loudest crowd reaction in Raw history. It's glorious.
Tying the Undertaker to his own symbol.
The Raw after Survivor Series 2001 was a simultaneous CMOA for Austin and Ric Flair. For Flair, it was his return to the WWF after so many years and becoming business partners with Vince. For Austin, it was his almost effortless Heel–Face Turn one night after leading Team Alliance against Team WWF in the Survivor Series. Turns out that beating the crap out of Dirty CowardKurt Angle makes turning face real easy. Observe.
A championship match on Raw between him and The Undertaker received a 9.1 rating and a 17% audience share, by far the highest rated segment in Monday Night Raw history (yes, even higher than "This is Your Life" note In all likelihood, the reason that WWE doesn't promote this segment in favor of "This is Your Life" is because Vince McMahon has always been trying to push the fact that his company is more than just a wrasslin' business, it's an ENTERTAINMENT business. ).
After Brock Lesnar attacked him and stole his ATV, Austin appears on the last Smack Down before Wrestlemania XX and face off with the Beast himself. Paul Heyman sends the Smack Down locker room to stop him but no one listens to him, not even Heyman's other client, Big Show. Austin enters the ring and beat the crap out of Lesnar, even causing him to bleed, and take back his ATV. Probably the closest thing we have for an actual Austin vs. Lesnar match.
Austin stunning both Goldberg and Brock Lesnar after their match at Wrestlemania XX. The fans are all over him, considering this is Lesnar and Goldberg are leaving the company after this.
Being the only wrestler to win the Royal Rumble three times, a record that has yet be broken.
Heck, anytime Austin delivers a stunner to anyone (especially Vince) is a CMOA itself.
Meta-example, Austin stunning Donald Trump at Wrestlemania XXIII is consider a CMOA, since he actually attacks a future US President.