How many stars and galaxies can be seen by the naked eye?
In the best sky conditions, the naked eye (with effort) can see objects with an apparent magnitude of 8.0. This reveals about 43,197 objects in the sky.
There are 9 galaxies visible to the naked eye that you might see when observing the sky, and there are about 13 nebulae that you might see.
Sources:

The Bortle Dark-Sky Scale - John E. Bortle
How many stars are in the sky? - NASA
Naked-eye galaxies - Wikipedia
List of planetary nebulae - Wikipedia
List of diffuse nebulae - Wikipedia