Hawkeye staring down a group of mobsters who threatened to kill everyone in his apartment block in Hawkeye #6. The results aren't shown.
In the first issue, there was also him saving 'Pizza Dog' by stopping the driver who was about to hit it. How does he do that? By tossing a penny through the guy's car window, smashing it, to get his attention. There's pretty much one awesome moment every issue.
Hawkeye currently holds the distinction of being a member of the Justice League, the DC Universe's resident superhero team. Yes, he beat out other more notable heroes like Captain America, Iron Man and Spider-Man to get that slot to do so. How he does it is pretty epic as well: he and The Flash survive Krona's One-Hit Kill on both the Avengers and the JLA, and take the supervillain down.
Avengers Annual #16: After the Avengers lose The Grandmaster's unbeatable Cosmic Chess Game for the fate of the universe, Hawkeye takes advantage of The Grandmaster's gambling compulsion by proposing one last game of chance for everything. He rigs it. That's right. Clint Barton saved the universe with carny sleight of hand.