If you want to make icons (such as a favicon.ico for your website), check out the freeware: Greenfish Icon Editor With this tool you can cut and paste .PNG etc. images into the editor and save as .ico

Also, you can create multiple-sized icons for use in Windows where the icons range in size from 16x16 pixels up to 256 x 256 pixels. So you can create icons for applications, or for desktop shortcuts from say box art of your favorite game.

In the Windows explorer document view, you can scroll the list view control to go from small icons to extra large icons to test out your icon.

And for the web, if you create a 16x16 pixel icon and call it favicon.ico and upload to your home directory, it should show up in your browser tabs.

Another thing to try is Pixel Art where you try to create artwork by directly editing pixels. Take this even further by creating a game within an icon (yes, it has been done - using Javascript!).