The Future Trilogy (ie. the PS3 games, more specifically only Tools of Destruction, Quest for Booty, A Crack in Time and Into the Nexus) aren't very childish.

Ico and Shadow of the Colossus, God of War (bought the saga collection so I'll be playing that), Jak and Daxter, Ratchet and Clank.

I'm kind of interested in playing the Uncharted series, since people claim it to be a good series.

Though the one I really want to play is Gravity Daze. I like the design of the character and the concept sounds interesting. I have the game and the system, so I just need to play it, haha...

I'm not sure I would use "childish", though I get what you are saying about R&C.  But those games are actually refreshing to play.  It's just no-thrills fun, all of what you want and nothing you don't. 

None, I tried most of them, and the few I didn't, like infamous, is because I have no interest at all.

Gravity Rush - it looks really fun
Littlebigplanet - They say the controls are floaty but the games look fun and charming

Tearaway unfolded. Soon to be rectified as it's next on after I complete Unravel.

Folklore, White Knight Chronicle, Rule of Rose

Hmm, I think I played all the ones I wanted to. Crash comes to mind in terms of the one I neglected the most. Although I did want to get more into Gran Turismo. I have 3 and I heard that was the best one.

I'd honestly recommend either getting the Uncharted Collection for PS4 if you have it, or if you don't, skip 1 and start with 2. The controls in Uncharted 1 have aged absolutely terribly (imo, obviously).