I was pretty sure the answer was NO, and hence google gears, adobe AIR, etc.
If I was right, then how does http://tiddlywiki.com work? It is persistent and written in javascript. It is also just a single HTML file that has no external (serverside) dependencies. WTF? Where/how does it store its state?
Tiddlywiki has several methods of saving data, depending on which browser is used. As you could see in the source.