If you airdodge you keep your double jump if you didn't use it.
You DO keep your second jump if you airdodge and haven't used it yet.
This is very useful for Samus/Link/Ylink because you can airdodge in any direction (including upwards), use your tether recovery to hook onto a wall, and be able to double jump afterwards too.
Just something random too: For Fox/Falco, if you are hit out of your up-b while you are charging up your fire and you haven't used your second jump yet, you will be able to use it once you're able to move again.
Anyways, as a response to this thread... Sometimes I airdodge in place if a Samus shoots a charged shot at me and my shield is too low and I don't wanna block it, and if I roll towards her it would put me in a position to be punished by her. I guess you could use an airdodge in place for similar situations lol.
the **** is triangle jumping
For those who don't know what triangle jumping is:
http://www.youtube.com/watch?v=iDJyIanqXJs#t=1m36s