When fly fishing I do something that sounds like what Cappy does, snapping the fly line the way you snap a blanket to create waves in it.
In a boat, I first get as close to the snag as possible and submerge my rod tip as deep as possible and tug in the opposite direction of the way I was retrieving/trolling. If that doesn't work I will let out a lot of line and paddle/row/motor in the opposite direction. I then tighten the drag and point the rod directly level with the line so as not to put pressure on it, then yank. Sometimes it comes loose, sometimes that's where the line snaps.
From shore I will pretty much the same thing that Simplify says he does in his OP.
I know there are tools that some anglers use with some degree of success but I've never tried them.