What are some theorems which might explain (i.e., generatively) why real-world data might be expected to be normally distributed?
There are two that I know of:
The Central Limit Theorem (of course), which tells us that the sum of several independent random variables with mean and variance (even when they are not identically distributed) tends towards being normally distributed
Let X and Y be independent continuous RV's with differentiable densities such that their joint density only depends on $x^2$ + $y^2$. Then X and Y are normal.
(cross-post from mathexchange)
Edit: To clarify, I am not making any claims about how much real world data is normally distributed. I am just asking about theorems that can give insight into what sort of processes might lead to normally distributed data.