The user has a tremendous lung capacity and/or ability to use the oxygen very effectively enabling them to hold their breath for extended periods of time while staying active. This may also include birdlike lungs that allow the user to keep their lungs constantly filled with fresh air.
While this ability allows one to survive extended periods without breathing, it doesn't mean they don't need air, but they can survive for longer periods without it. Sooner or later they are gonna need to breathe.
Free-diving is mundane and learnable version of this power.
Superman (DC Comics)
Supergirl (DC Comics)
Martian Manhunter (DC Comics)
Miss Martian (DC Comics)
Power Girl (DC Comics)
Kryptonians (DC Comics)
Martians (DC Comics)
Dheronians (DC Comics)
Tamaraneans (DC Comics)
Starfire (DC Comics)
Blackfire (DC Comics)
Kwai Chang Caine (Kung Fu)
Krillin (Dragon Ball)
The Saiyans, including Vegeta and Goku (Dragon Ball)
Many Bishokuya (Toriko)
Forsaken (World of Warcraft)
Alek Filipov (Ripley's Bureau of Investigation)
Mermaids and mermen (H2O: Just Add Water and Mako Mermaids)
Louise Chatham; temporarily
Julia Dove; temporarily
Gracie Watsford; temporarily
Charlotte Watsford; temporarily
Guybrush Threepwood (Monkey Island); limited to 10 min.
Jigglypuff and other "Balloon Species" Pokemon (Pokemon)
Tidus (Final Fantasy X) and other Blitzball players
Rikku (Final Fantasy X)
Wakka (Final Fantasy X) and other Blitzball players
Yuna (Final Fantasy X-2) and other Blitzball players