I made a little paint program in Java. Drag the mouse to draw, click a color in the palette, and keep drawing. It is not going to replace Paint, but it is mine.
The applet listens for mouse presses, releases, and dragging. The palette is an image with different clickable coordinate regions; choosing one updates the current AWT Color. While drawing, the paint method places small filled ovals at the mouse position. The update method goes straight to painting so the drawing is not cleared on every normal repaint.
There are some fairly obvious limitations: the brush is simple, the palette is fixed in place, and this is not a document editor with an undo stack. Still, it is fun to make something where the result depends on what somebody else draws rather than on a score or a correct answer.