How Do You Make A Cake Without Vanilla Extract?

Yes, absolutely. Most cake recipes call for about 1 teaspoon of vanilla (or vanilla essence or vanilla extract) but it will not change the recipe if you don't have it. You could use another flavoring if you have it, but you can also leave it out and the cake will still taste good. It's a very subtle flavor (1 teaspoon in an entire cake) and nobody will miss it.

I use a flavored yogurt instead, and it turns our great!!

I usually put almond extract in my cakes if I don't have vanilla

Soo I'm going to try the vanilla yogurt because I don't have vanilla extract :)