Goku, Gohan, and Vegeta all unlocked their Super Saiyan forms in times of great anger, and got significant boosts during times of great stress... until after Cell Saga. Goten and Trunks, whose greatest stress triggers have to do with their toys, unlocked Super Saiyan forms, throwing all of that out the window.

Vegeta explains that rage is the source of Super Saiyan forms, too, in Super. I think it's been mentioned before, but I don't remember where.

I'm not sure if this applies to beings other than Saiyans, but seeing as how everyone powers up the same way, squatting and screaming and their forehead veins bulging, like they're trying to let out the biggest hard bowel movement in the history of the universe, tells me that it's at least somewhat similar.