I liked dragging a selection box on the desktop and seeing how thin of a line I could turn it into. When it was perfect the line would dissapear and just have one pixel on the top and bottom. It was also fun to draw the smallest possible box around random things on the desktop wallpaper. I did that with the windows 7 stock wallpaper a lot.
My 5 year old has done this a couple of times as well - I just has to adjust my semi-crazy mouse speed to her. :) I even saved the pics.
Another thing I distinctly remember is watching my das defragmentating the drive. I know that I at the same time hated it because it meant that we could not play games, but it was also strangely mesmerizing...
I remember drawing the Death Star and lots of TIE Fighters. One version of paint had this line tool that produced the hyperspace lines effect. Nowadays, I dabble with pixel art in Aseprite.
I still occasionally do this if I am on the phone with someone and need something to do with my hands that doesn't take much brain power or make any noise.
I do remember. I used to fill the background with a basic color and then grabbed the free-form selection tool. I'd move my mouse around like crazy to make this shapes and then cut it out. But sometimes, my old Pentium II PC would freak out for a sec if the selection was too wild. Fun times.