I want my player profile stored in that memory.  When I turn on the Wii and it detects the controller, the two devices should sync up and automatically assign my name into the game.  Imagine entering your name or initials one time during initial configuration and then never having to do it again on a per game basis as we do now.  Imagine taking your Wii controller to a friend's place and having his Wii automatically pick up your identity from your controller.

Let's go a little further.  It may be a lot to ask of 6KB, but how about if any unlockable characters or levels you obtain in a game were "stored" in that controller memory?   Not the actual levels or characters themselves, of course, but the flags that notify the Wii that you've unlocked such things.  Imagine unlocking a secret character in Super Smash Bros. Brawl, going to a friend's place with your controller, and being able to select that hidden character on another Wii because you've already unlocked it on your own console.  What if you were the only player who could select that character because you're the only one who has unlocked it?  Or maybe we should share the wealth; by bringing your Wii controller to a friend's place, that secret character becomes permanently unlocked in other controllers in the room for everyone to use (even after you take your controller and go home).

I don't know how much of this wish list is feasible.  6KB is not very much memory these days, but in the right hands and with the right data compression at work I don't see why these ideas couldn't be implemented.  If the Wii philosophy is all about playing together, then why not make it as easy to bring identity and achievements together as it is to bring people together?