Quotes: Non-Standard Game Over

You've met with a terrible fate, haven't you?
The Happy Mask Salesman, after the Moon crashes down on Termina in The Legend of Zelda: Majora's Masknote 

And so the world drifted towards its fated destruction...
— The consequences of Refusal of the Call in Golden Sun

Hellsinker, if you time out the Segment 7 boss with one life left, Rex Cavalier

The Stars Say
You fell in a hole.
Try Again
Rhythm Heaven Fever, if you fall into a pit in "Night Walk"

"I'm outta here!"
Sonic the Hedgehog, Sonic CD, if you idle for three minutes

Do you recall my words to you before? "The coming year is a turning point in your destiny...If the mystery goes unsolved, your future may be forever lost." I meant precisely what I said. Defeat in battle is not the only way your journey may come to an end...Please do not forget this.
Igor, Persona 4

This is roughly one minute into the game and makes for a pretty cool ending that needs to be featured in more Hentai games if you ask me. It's basically you taking the option of "no, I don't want to play this game" and the game apologizes for being so shitty and you're free to leave.
Zack "Geist" Parsons, while reviewing the H-game "Gloria", on the game's option to Refuse The Call

None are more contemptible than those who defile the way of Bushido. - Kannagisai

But the future refused to change...
Chrono Trigger, if you lose to Lavos

The Rebel Flagship is within range of the Federation Base. All is lost, they've won.
FTL: Faster Than Light, if you let the Rebel Flagship reach the Federation Base

Hm...? The last bribe is still on your tab. If you can't pay the bribe, I can't possibly revive you. You there, jailer. Throw this youth's soul into the mountain somewhere over there.
Charon, Shin Megami Tensei IV, if you die while still in debt to him