I'm an old school guy an abhorred the idea of Action Points when I first read about them. Then I played Savage Worlds, with its sister-mechanic Bennies. In Savage Worlds you can use them to Soak damage (avoid some or all wounds from blows), to un-Shake (a wound condition similar to stunned), and to reroll certain rolls (skills, attacks, etc). We also use them to add a flat bonus to rolls - a bigger bonus if you declare the Benny use prior to the roll, a smaller bonus if you choose to use it afterwards.
As both a player and a DM, I think Bennies rock. My players do cool, heroic things they might not try otherwise, because they have a small safety net they can use to weigh the odds in their favor when trying them. Makes the game more fun.
Heck, I imported the mechanic into C&C, and will import it or something similar into most any game system I ever run.