I created an app icon for a business I run called The Useful Stuff. I put my initials in the background around the edge of the app icon. I also added a shadow to the word 'Useful' to make it stand out further when the icon is small.

I first created a 120px icon, then a 16px favicon, followed by 300px and 600px icons. Then I made another 120px icon in a bright orange.