Does anyone ever do anything with their old saltwater when they do water changes or do you simply pour it down the drain? I was thinking it might be handy if you're starting a new tank, want to cure some rocks, have a quarantine tank, etc.

Sure. I read once about pouring it on your driveway (careful not to get it on your car - salt can cause rusting) so I've done that some. Salt is really good for cleaning things like that and it keeps algae/moss/weeds from growing on the driveway.