The current game I'm playing in is the only one I've ever played with Action Points. We're using a house rule or variant for Action Points within 3.5 D&D.
Usually it's 'save my bacon' usage, though we have had a few 'heroic' uses, where a certain action simply has to succeed. Rarely though does it matter; the ones where 'the action has to succeed' don't, because it's still a roll - rolling is still involved and more often than not it seems that that's the time the action dice come up '1'. But they are useful sometimes, especially when it's used for 'um, give us a hint as to what we should do?'. I've played a character to 11th, so far, so I've seen a fair amount of action point usage.
Hero Points in Arcana Unearthed were much different. Since you could only gain them with heroic actions instead of just by leveling, people attempted more heroic actions. Over the course of a 14 month campaign, they probably received hero points twice over all. Because they are so rare, they were used for dramatic effect - I let someone bring someone back from the dead with her healing aura because she spent a Hero Point. Another was used to live through blowing up an evil alchemist's tower - he found the room where all the explosive powder was being made, set it afire, then jumped out of a ten-story window as fire blew out around him.