First of all, we all should reuse and recylce anyway. We're duty bound to Earth to do that.
Second of all, yogurt cups are very reusable, it will be a shame not to do so. Just wash each cup well after use so you don't attract ants. You can use it to organize coins in, or small screws in, or even thread, pins, and keys in. You can even use them to collect those pesky 5 and 10-centavo coins they give us when we shop in malls which nobody else really accept. At least you can have these exchanged in banks once you've collected a ton and not lose money.
Your kids will also benefit from reusing yogurt cups. They can house arts and crafts materials (buttons, crayons, brads, etc) and even be used as paint pots. The really imaginative can even make musical instruments from these cups!
But if you'd rather throw them away, make sure you do in bags/can marked for recycling.