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

SPIRIT OVERLOAD
YOU GOT INSANITY.
YOU MUST RESHAPE ONESELF FOR ONCOMING ASPIRANTS.
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

One may follow a damned path, but that is not the way of Narukagami.
Kannagisai

Those who stray from the true way, follow a damned path.
Kannagisai

Seek to save your life and lose it. Through death one finds the way of Narukagami.
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

Ha, ha, ha! The world is mine!
Dr. Muckly, NAM-1975, if you lose to him

In my fading consciousness, a single doubt remained. Were the allied forces really late, or...?
Then, right before the end, I thought I saw countless white angels circling down from an endless heaven.
Einhänder, if you run out of time during stage 6.

"This is all a bad dream... and you're never waking up!
HAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHA- (game closes)
Flowey, Undertale, if you lose to him in the final battle