Sidney and his compadres thought of there being three genres: poetry, prose, and drama. Nowadays, the schematic is vastly more complicated (and we apply that complication retroactively to the Elizabethans as we study them).

What about comedy and tragedy within drama? Pastoral and epic within poetry? Romance in prose and verse? I know early modern writers made distinctions between these literary kinds; if they weren't genres then, what were they?

And although it's very tangential to your post, I've always wondered why some genres go so far out of style as to be effectively defunct. If you know of any convincing theories about why this is so, I'd be very interested.