Hah, as I type this, I'm fixing the left analog stick on one of my controllers. I just need to find the crazy glue, and I'll be done.
Here's why the sticks get worn out. I'm waiting for my optical mouse to come in the mail, so the ball mouse I used made everything look sloppy.
http://jigoku.studio-zoe.com/temp/gcnstick.pngIn figure A, we see the analog stick without the plastic cap on it. Note the stick in the middle.
In figure B, a closeup of the stick. Two posts come off of it about a quarter inch down. Those posts go through notches, and when you move the stick, it pulls on these notched parts and blah blah blah.
In figure C, you'll note that the post looks chewed up. This is from constantly pushing the post against the notch. It gradually wears away. Near as I can figure, gluing the post into the notch CAREFULLY (if you gle everything together, you just killed the stick mechanism), the stick should respond normally... but super glue doesn't held up to great amounts of stress. Anyway, the controller should work fine after that, and the only problem I forsee is the stick not standing perfectly straight up when at zero position.... but that's not big deal, it won't be severe.