Many games only require simple round counters. Smaller counters can be made the same way from dowel. Stain the counters as required to produce different colours and then polish them up. Since the counters are so easy to make, it's worth having at least one spare of each colour. If you want to make a chess set, you're on your own.
Dice are very fiddly things to make accurately, but can be sawn from an off-cut of an old plank.
You will have to keep checking the widths across the faces, and sandpapering until the dice are good cubes.