Savage Worlds, which uses cards to adjudicate initiative. This is an excellent use and takes good advantage of the strengths of cards.
What are those strengths? First, they’re easy to use: flip a card and you’re done. No fumbling around with a pile of dice, worrying about them rolling off the table, and leaning in close to read it. Your normal playing card is designed to be easily read from across the table (the job made easier since it only needs to convey two pieces of information: suit and value), which means you can flip your card and everyone can see when your turn comes up.
Unfortunately, using a stat modifier on the card ruins things a bit; you no longer use the value shown, but now have to figure out what an adjusted value is. So you want to use the raw card as much as possible (for instance, using multiple draws for characters with a high stat, allowing the player to pick which of the cards they’ll use).
Cards work best, as I’ve already said, when they convey very small amounts of information easily gleaned from across the table. However, you’ll also want all the necessary rule info on the card as well, and those two optimizations can be mutually exclusive. It’s best to keep the effects of cards as broad and simple as possible, or as obvious as possible (such as cards describing the day’s weather, for instance).