If you are absolutely set on not using any server-side language you do have options, however, depending on the game you are trying to build it's probably better to use an actual database on a server and pass information back and forth via a server-side language.
Anyway, cookies are always an option and if you want to make this game work for as many users as possible it would be your best client-side option. But if you aren't too worried about losing a few potential users who are still on old, outdated browsers you can utilize a few HTML5 storage methods that would make your job a bit easier and ultimately yield better results.
First check out: http://www.html5rocks.com/en/features/storage
Realistically you have 3 potential options through this. LocalStorage, IndexedDB and Web SQL.
The localStorage route would probably be the most difficult to work with as it's most similar to cookies, giving you a name and value pair to store variables. LocalStorage will still cut out some old versions of certain browsers (like IE7) but will be the most widely accepted HTML5 method for storing local data.