My favourite game in the whole wide world - the "country game" (or any other geography term - cities, states, provinces, bodies of water). You begin with a term (Canada) and the next person must begin his or her answer with the last letter (A = Amsterdam) then the next person (M = Mexico). You can't repeat a term or you are out.
Or name countries from east to west without going backwards (Canada, France, Italy, Russia, United States of America). You keep circling the world.
Or backward skip counting (begin at 118 and count down by 3).
Or look at a nearby sign and try to create as many words from the sign (for example, Swiss Family Robinson = robin, son, sin, in, bin, win, fin).
Have fun!