In most cases no. In baked goods, eggs are an emulsifier, a binder and a leavener. They also have a role in preventing cakes from sinking in the middle (the higher the protein content of the cake, the less likely this is to happen).
Yoghurt is not a leavener; it is not possible to whisk in air bubbles until it's foamy in the same way that you can for an egg. (So this rules out genoise sponges, meringues, fatless sponges etc...)
Yoghurt is acidic, eggs are not. This extra bit of 'acid' in a recipe can through off chemical-based leavening reactions, resulting in some very peculiar tasting cakes. (Which rules out any baked good leavened by baking powder).
Yoghurt has a distinctive taste, which eggs do not have.
Eggs give baked goods a golden-yellow colour, which would be lacking if they were not used in the recipe.
Substituting an egg with another ingredient is actually very tricky, since eggs are pretty much unique in their properties. (Some people suggest using "blended up tofu", some people suggest using the gel from soaked flaxseeds as an alternative, but the results are invariably a bit weird compared to using eggs). If you need a recipe which does not use eggs, you'd be much better off finding a recipe which is designed not to need eggs, than trying to adapt a recipe which does.
Replace one cup of yogurt with: 1 cup sour cream OR 1 cup buttermilk OR 1 cup sour milk.
yes, a go-gurt they are surprisingly delious.
A great substitute is soy yogurt.
Buttermilk.
you can substitute yeast with curd /plain yogurt
Sour cream.
You can use Sour Cream of Mayonnaise as a substitute of yogurt.
They proposed to use yogurt as a substitute for meat in school lunches in 1996.
Plain yogurt is usually a good substitute for mayo.
yes
Yes, if you want to.
Thick Greek Yogurt or another kind of unflavored yogurt should work fine.
Frozen Yogurt which is really tasty!
Yogurt is not a good substitute for butter in any recipe; yogurt is lower in fat, higher in liquid and far more acidic than butter. These qualities make it very different to butter, hence it's not a good substitute.