Most of my games are upbeat, and some of them are downright cute. I own very few grimdark video games, and I tend to avoid games where the main character has a gun at the ready.
Sakura Wars 5 strives to be crazy-awesome, with deliberate anachronisms and plenty of over-the-top stuff. In one of the best scenes,
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Oda Nobunaga's castle appears in the middle of New York circa 1928... and the characters aren't even surprised!
A Dog's Life (PS2) is not taking itself too seriously. While it's not an especially good polygon action game, it's also charming and amusing, as it pits a dog against cartoon villains.
Katamari Damacy tries to be ridiculous. Not only does the main character have to roll up the most random, insane objects, but the premise of the first game boils down to "God gets drunk and destroys the universe. You clean up his mess."
Team 17's main games are a bit off. They made the classic Lemmings (cute creatures endure puzzles and often die) and the equally classic Worms (cute creatures blow each other up). Lots of comical voices in both games.
Hatoful Boyfriend is not taking itself seriously. It's a reverse harem story, but every male haremette is a bird. Comedy ensues.
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But the game will occasionally surprise you with serious endings.
Maniac Mansion takes a simple sci-fi/horror premise and makes it seem wacky. There's some crazy logic puzzles, and the characters are funhouse mirror versions of classic archetypes.
Finally, there's a couple of classic platform games that have nonsensical actions and mechanics. Ever thought about why things happen in the classic Super Mario games? And if you remember the Bonk series, then you probably think Mario is normal by comparison.