Some RPGs (7th Sea, Savage Worlds, FATE, PDQ, etc) include some small budget of tokens you can spend for the rolls that really matter. Bennies, Drama Dice, Fate Points, Aspects, etc. They are often represented by poker chips, glass beads, or unusually-colored dice. You usually get 3 or 4 of these things at the start of each session, and opportunities to earn a couple more as you play.
In their simplest form, these give a bonus on your roll, or maybe a reroll. The point of this is so that you're not screwed when the dice misbehave at a critical moment. My life depends on this roll? I'd better spend a Bennie. The bad guy's getting away? I'd better spend a Bennie. The plot stalls out if I don't get this NPC to confess? I'd better spend a Bennie.
In many of these systems, you can also spend your Bennies to gain narrative control. Each point spent lets you add a detail to the setting, improvising some fact or development that is to your advantage in a way that is more flavorful (and flexible) than just another +X to a die roll. It's all about empowering the players. If you had enough Bennies, you could totally take over the game and leave the GM in the dust.
The GUMSHOE system, in a nutshell, is a game where your entire character sheet is nothing but Bennies. It's like starting every session with about 80 Bennies per player, and I find that to be awesome.