I think this has been well answered.
Cedar and spruce are most common woods used. That would include Englemann/European spruce, Sitka (Alaskan) spruce, conventonal (Eastern) Cedar, and Western Red Cedar.
Other top woods used include plywoods (all different kinds) and redwood. High end classical guitars are sometimes built with "double" tops, which are actually comprised of a sandwich of conventional tone-wood with nomex synthetic fiber on the inside to save weight and increase volume.
There are classical guitars made with carbon fiber tops now. Historically, there have been acoustic guitars made with plastic tops. Macaferri, famously, made some. See here: https://www.youtube.com/watch?v=cuB2hprvfdc
Mahogany, Koa, and Maple are used as tops in some acoustic guitars. I've never seen classical guitars with these top woods, but I'm sure there are indivdual examples out there. I'm also sure there are all sorts of one-off instruments built with tops from other varieties of wood.
See here for an acoustic (not classical) guitar made entirely from ONE 2x4 (which is Southern Yellow pine).
It doesn't (IMO) sound that good, but I still give the guy 10/10 marks for doing it, and I bet someone who was an experienced luthier (vs a skilled amateur) could probably build something that sounded much better from the same materials.