Ahhh, the age-old question
I generally keep my might for heroic actions, particularly moves and strikes. I'm very careful about calling heroic combats, especially as my regular opponent almost always has fury; it's never nice to have a hero blow a might point on failing to kill a moria goblin. However, I use strikes alot, although mainly do so to counter my opponent's bigger heroes, I often don't counter if it's just a captain. I've only ever used a heroic shoot once and never used a heroic accuracy, so you'll have to talk to someone else for help there.
If my hero has a lowish defence and fate I like to keep a might point in order to win a fight, but unless it's aragorn's/bolg's/narzug's etc. free one I don't like to use might on winning fights, only when it's a fight for survival: when it's a trapped hero on one wound. no fate it's time to ready my pencil and paper to jot down some expended might. On the contrary, my might points are often used on knocking off wounds from dangerous heroes, though this may be because I almost always play Gulvahar, who gets much less dangerous as he loses wounds. That being said, wounding big heroes does tend to make your opponent use them a little more carefully, which can be used to your advantage.
A general tip I have for using might to wound is always look at the scenario rules and see if you'll get a point back for killing a hero; if so, you may as well put a point towards wounding a model if it's really bothering you as if you have support it may die. This has worked wonders for me before and it's an easy thing to forget.