Links are all for games that can be played on screen.
Age range: preschool and up
At the very beginning I was just looking around for some preschool games that didn't require mouse clicking for my two year old so that he could play by himself without my help for a while. We came across this great train game that he enjoyed quite a bit:
Train in the Train Yard
Here are some links to games that he enjoyed with my help but could also be enjoyed solo by ages three and up. Less than three and the clicking and mouse control are too advanced:
Easter Egg Colouring - This one only required help to click up a new egg onto the screen. Then the baby enjoyed moving the cursor around the screen on top of the egg. Whereever the cursor touched, a bit of the egg's design would appear. Spoiler: Save the yellow egg for last.
Writing Sheets - It's actually quite fun to try and stay on the lines using your mouse to write with. My two year old enjoyed guessing the numbers and letters I was writing.
The Sensitive Pumpkin - We enjoyed changing the pumpkin from a happy mouth to a sad mouth.
Easter Egg Hunt - We enjoyed counting to twelve. Just click your 'reload' button at the top of your screen to scatter the eggs and start over. First, we did it in English, then French, then Japanese. Finally, we finished in English. I expect he'll be able to hold and click the mouse to drag the eggs to the basket before he's three. This'll be a nice thing for him to do when I'm making dinner.