I run plenty of games that have this mechanic in them - fate points, hero points, bennies, fortune points, determination - and so on.
I like the effect they have on the game when players understand how to get them and when to use them - it adds an extra dimension to the fun.
The different systems all have different ways of calculating how many you get to start with and how many you can accrue. I think they work best when they are a limited resource and are hard to acquire - too many and you start to effect the balance of things. To my mind, they suit heroic play better than 'realistic' play. If you want your players to act in an heroic way, then fate points should be one of the tools that allows them to do this.