In reality it is not always this simple. Horses and donkeys can breed- producing mules or hinnys but these offspring are sterile. Another example of two different species breeding are carolina and black-capped chickadees. Again though, the offspring have a reduced fitness and the females are usually sterile.
So, for the most part, closely related species may be able to produce offspring (and the only way to know if that is possible to try to breed them), but if the species are truly distinct then their offspring will be sterile or have a reduced fitness.
