Thinking of games I've played recently, Dominion would work. Ticket to Ride wouldn't. On the Underground would, 1960 Making of a President wouldn't.
Normal Settlers wouldn't, but the junior version of Settlers would
The key thing is not drawing secret information from a shared pool. Dominion works as it's secret information from a non-secrete deck, which can be known by all players -- you just have to ensure to remove the right cards from play. If player A takes a Duchy, player B removes one Duchy from his set from play.
With Ticket To Ride there's no way to ensure that you don't get the same tickets on each side - secret information from a common limited source.
Normal Settlers would struggle with the soldier cards -- you can draw a soldier, but it could be roadbuilding or year of plenty. Junior settler has the same with coco cards, but those are played immediately so that works.
Obvioulsy open games, like Chess, Go, Backgammon, work. Games like Battleships and Guess Who, where there is secret information but no shared ppol would work too (ok you could both be guessing the same character in guess who, but that would be OK)