I have been running mutants and masterminds and really enjoy freely giving tons of hero points for cool actions, a witty comment and anything else that improves the game table. I already use hero points in Pathfinder, but how I give them out and the powers that they can invoke I like them as rare commodities. They usually only get them for gaining a level or finishing a full book of an Adventure Path. I want something in addition to these that would be given much more freely. I have been listening to the Glass Cannon Podcast and they stole something from 5th Ed they call them Bottle Caps where a player can use a “bottle cap” to gain a 5th edition term an advantage which allows the player to roll 2 d 20s and take the best result. I was thinking these could be given during game play, they would never carry over between sessions. (So they would be used each game session) This would push the heroes to do more things that are an improvement to the game, better roleplaying more creative actions and so forth. Do you think these would be a good thing or just an extra thing that players won’t think of because they already have hero points to deal with?
How well/often your players will use them depends on your players. I don't think anyone can answer that question for you.
As to what effects this could have on a game (assuming your players use them) it will, of course, reduce the challenge. Rolling twice and choosing the best is a pretty powerful advantage. Personally, I'd use it for saves most of the time.
Fundamentally though I question the need for this sort of thing. In my experience as both a player and a GM, doing cool things, making witty comments and everything else that improves the game table are their own reward. Also, I think trying to force them is futile and usually self defeating. If I make a witty comment because it feels like a fun thing it will probably improve the table experience, if I'm going around looking for something witty to say so I can gain a mechanical advantage for my character, it will probably be a whole lot less enjoyable for me and everyone else.