Despite all the answers to the contrary, this is indeed possible. However it is limited by browser support. You can use the new FileSystem APIs in the latest versions of Chrome, etc:
window.requestFileSystem = window.requestFileSystem || window.webkitRequestFileSystem;
window.requestFileSystem(window.PERSISTENT, 1024, function(fs) {
fs.root.getFile('mystorage.txt', {create: true, exclusive: true}, function(file) {
file.createWriter(function(writer) {
var blob = new Blob(["putdatahere"], {type: 'text/plain'});
writer.write(blob);
});
});
}, function() {
console.log("Could not access file system");
});
Since you only want the files for your own uses, this sandboxed approach will work. There are a few more hoops you need to jump through (requesting a quota, creating a Blob object) but those are covered by the linked article and will all depend on your requirements.