If we take the double slit experiment as a way of demonstrating the wave-particle duality, which types of particles would show an interference pattern?
For example, I know that electrons show such a pattern. But do protons, too? What about atoms? Where is the boundary between "wavey particles" and "classical particles"?
All of them. Even molecules show their wave-like nature, as does, in principle, every object. Speaking of these topics an interesting read about diffraction of C60 molecules is: http://www.univie.ac.at/qfp/research/matterwave/c60/
The point is that the wave-like nature of objects can only be observed at lengths comparable the object's De Broglie wavelength, defined by:
$$ \lambda = \frac{h}{p} $$
where $h$ is the Planck constant and $p$ is the object momentum. For an object moving at non-relativistic speeds you may remember that the momentum is defined as $\vec{p}=m\vec{v}$; the De Broglie wavelength is then inversely proportional to the object mass. The bigger an object is, the less relevant its wave-like nature is, and that's why in everyday experience we are not used to observing the wave-like nature of massive objects.
