Leaving aside the collectible and poker deck ideas, a great many recent wargames have been using card play to good effect. I'll point the reader to Volko Ruhnke and GMT's COIN series for excellent examples of this.
The trick with using cards in RPG play will be in keeping the referee/players relationship collaborative rather than competitive. If either side can "trump" the actions of the other, the collaborative story telling angle will soon be on life support.
Instead of "trumping" actions and events, cards could be used to modify or tweak the same. Because such card play could produce actions and events "outside" what the referee and players normally think or do, the results could "deepen" or "enrich" table play.
One mechanism would have the player(s) choose whether or not to play a card from among a small number. If the player(s) lay a card, the referee would then play a randomly selected card as a "counter". If cards are played, a replacement card is dealt at random to the player(s) and referee. Another wrinkle could have a player who rolls for "exceptional success" choosing whether they want that success applied to their action or if they want an additional card for their hand.
Let me use Across the Bright Face as an example. The referee has just rolled on the Mountain hex table for "Mine Shaft Entrance". Such an event triggers a "two tiered" decision. First, a die is rolled to determine if the shaft is wide enough for the ATV. Second, if the players decide to investigate the tunnel, it's direction is rolled for.
The players decide to roll for the tunnel's width and find it's wide enough for the ATV. They then decide to play a card which will allow them to choose the direction of the tunnel. This will allow them to cross the mountain hex both faster and in a direction of their choosing.
Because the players chose to play a card, the referee selects a card at random which will modify the players' card, the players' choice, trigger another event, or cause some other action. The referee's card could change the tunnel's direction, speed the players' passage through the hex, trigger another event in the hex, impose a malfunction, remove a card from the players' deck, etc.
While the players' cards would generally be helpful, the referee's cards could either help or hinder. That chance of being hindered means the players would have to decide whether it would be worthwhile playing a card for it's benefits.