When would you use simple linear regression?

You use it when the relationship between the two variables of interest is linear. That is, if a constant change in one variable is expected to be accompanied by a constant [possibly different from the first variable] change in the other variable.

Note that I used the phrase "accompanied by" rather than "caused by" or "results in". There is no need for a causal relationship between the variables.

A simple linear regression may also be used after the original data have been transformed in such a way that the relationship between the transformed variables is linear.