Or work through the alphabet naming different animals. Or countries. Or given names. Or flowers.
Then there is Fizz-bang. You count up from one, each person saying the next number. Simple - except that whenever you reach a number that divides by, say five, you say fizz - one two three four fizz six seven eight nine fizz and so on.
To make it more difficult, you can then also add "bang" for numbers that divide by another number, and if they divide by both numbers you say fizz-bang - one two three bang fizz six seven bang nine fizz eleven bang thirteen fourteen fizz bang seventeen eighteen nineteen fizz-bang twentyone . . .