You mean RPGs with C&C? I'm sorry but you'll have to be more specific.
Kinda, yes. Specifically C&C about the PC's personal stuff like goals, dilemmas, personality, story, etc. A "Planescape Torment in tabletop form" description would not be that far from the target?
What RPGs are there to challenge PCs concepts, convictions
Well, D&D had the Helm of Opposite Alignment, potentially turning you from a Lawful Good paladin goody two shoes into a Chaotic Evil demon spawn.
Does that count as changing a PC's conviction to you?
I remember there were also ways to change alignment during the game.
Oh, have you tried Wraith: The Oblivion?
Some dark stuff...
I'm referring to games that has that kind of PCs challenging as an integral part of the core gameplay loop, usually supported by mechanics. Pendragon is the most popular I can think of. But there are others like say, Unknown Armies, Smallvile, Dogs in the Vineyard and Masks: a New Generation. Ever heard of those?
I'm out of the loop here and would love to see what new games cater to that playstyle.