Make "rain art." Have your kids draw on paper with water-soluble paints or markers, then put the papers outside to watch the colors bleed.
Sing in the rain.
Go mud sliding. This isn't for the faint of heart. But if you've had a lot of rain this season and it's not too cold, change your kids into their play clothes and let them slip and slide in the mud. Just hose them off before they come inside again.
Bake a mud pie.
Do some "science" experiments. Have your kids put a measuring cup outside to measure how much rainfall you're getting. They can check on them every hour and note the changes.
Try wet chalk drawing. As long as it's not too cold, let them take their sidewalk chalks to the wet sidewalks.