Eggs in Baking has specific purpose, depending upon the recipe. Once you evaluate it, making a substitute is relatively easier.
The substitution might differ depending on whether you are planning cakes, cookies, breads etc. Here is a comprehensive chart that you can use as a guideline to make the necessary substitutions.
But keep in mind that though such substitutions work very well in most of the cases, there might still be some compromise in the taste and texture to the finished baked goods. Making smart substitutions will help to minimize the difference in taste and texture. Check out the list below which elaborates on the kind of substitutions to make.