My kids are all between 1 and 3 (and my 4 year old son) and some of their favourite games are: sleeping bunnies (they could play this all day), simon says (I expand this and they hop like bunnies, slither like snakes etc), red light green light, rolling a ball to each other in a circle, ring around the rosie (once they do it a few times they get it and they love it), and for circle time anything that involves a puppet show is a hit...I get the puppets to teach numbers, shapes, etc.