You have two options:
- You have a a Web server and know how to program a server-side application, in PHP, Python, Java or whatever language is allowed by your ISP;
- You don't have this luxury...

In the first case, you can write an application that get the high scores of the players and store them, ready to re-display them, perhaps with comparison with the other players (top 10, top 50 or whatever). If the server is the one that provides the applet, no need to sign the jar.

In the second case, you have to sign the applet (that might discourage some users), and to ask the user where to store the score file (you can use System.getProperty("user.home") to get a relatively system independent location, but I discourage that as it ends up "spamming" this top folder).

Ah, actually, as you suggested you can have a third option (never tried it): communicate with some JavaScript on the page your applet is, and ask it to set a cookie.

I'm trying to solve a very similar problem here, and in my case the solution I'll need is the first option: a server-side application. I'm writing a Processing applet where users can assign colors to various things. I'd like the user to be able to save her personal colors (ideally under a username of her choosing), retrieve them later, and share them with others.

I'm a pretty quick study with new programming languages, but I've never written anything in any of those languages (Python, PHP, etc.) so I have two questions:

1) Which language would you recommend for a simple task like this?

2) Where's a good resource for learning to write server-side applications (with code snippets, etc.)?

1) PHP, because there is a high chance it is available on your host. Double check, though. Java is another option (you might be already familiar with the language, but you need to learn J2E) if it is available.
2) The Internet. Lot and lot of resources around...

Thanks for the lightning response!

I checked with my web host, and it looks like they speak PHP, Java, Python, Ruby on Rails, and other languages.

I'll google PHP and J2E and see if I can RTFM. ;-)

Thanks again!