I have two questions about the responses here:
First, two posters mentioned that it's important for a man to teach his son the difference between a woman and a lady. Obviously, as Johnniet's post reflects, there are some fairly obvious reasons for knowing the difference. But I'm wondering if, beyond the realm of potential sexual opportunities, knowing the difference would create a divergence in treatment. In other words, to what end will this knowledge make a difference aside from long-term versus short-term relationship potential? Are you teaching your sons to be a gentleman sometimes (when they're in the presence of a lady) or all the time (respect her even if she doesn't respect herself)?
Second...
"How to suck up to powerful people who you despise, but have to work with."
I'm open to hearing any lessons you've learned in this regard (aside from just plain
sucking it up).

I'm thinking that I might learn that one in my next life (or in the afterlife).
I also think that most of these lessons would be very relevant to girls also. Don't ever underestimate the importance of the father/daughter relationship. Girls love their dads.
Here's my list: (Trying to focus on men specifically.)
How to do basic repairs, ie, plumbing, electrical, structural, etc..
How to use most tools. (I'm amazed by how many men can't do either of these and don't want to learn either.)

A strong, confident handshake (girls too)
How to deal with various emergencies (dry runs) (girls too)
How to fight. (very important.) (girls too)
How to shoot. (girls too)
How to pitch a tent.
How to hunt/fish.
How to work on a car. (girls too)
How to cook on the grill.