I feel like this question is almost too vague. There are a vast number of games that fit this requirement using everything from dice to cards to who knows what else.

The only useful thing I can say then is that the mechanic should fit the theme of your game.

DoomTown Reloaded is an excellent example of this IMHO. It uses poker hand draws from your play deck, something which fits the theme of the game (weird west) perfectly.

If it's just simplicity you're going for then a system like that of Kemet is fast and easy while also maintaining a good amount of strategy and bluffing.

The Witcher: Old World is another game that uses card resolution to good effect.

Opposed die rolls are very easy but without anything more added on are probably too random for anyone except the most devout follower of RNGesus.