One of the most popular posts on macintoshhowto is this 6 year old article on how to clean an Apple mighty mouse. It’s had over 200 comments!
Here’s a video so you can see what it looks like.
Apple recommend rubbing a piece of paper over the top of the scroll wheel, but I find turning the mouse upside down and running it round in circles is much more effective. The paper must be new and clean. An old piece of paper doesn’t work.
I’ve been using this method 2-3 times a year for 6 years and my Apple Mighty Mouse with scrollwheel is still going strong.