There are no electron _particles_ moving around an atom - this is the old, insufficient Bohr model, so nothing that would collapse. It is very well understood why atoms are stable - the ground state is a stationary state that can live indefinitely (unless the nucleus decays).
There is no empty space around a nucleus, as in Bohr's superseded model. According to quantum electrodynamics, the space is filled by an electron _field_ around the nucleus which neutralizes its charge and fills the space defining the atom size. What is displayed by a field ion microscope
http://en.wikipedia.org/wiki/Field_ion_microscope is the boundary of this field. But this boundary is not perfectly defined but a bit fuzzy, more like the surface of a piece of fur or of a cloud.
If two atoms or molecules touch, the volumes occupied by their electron fields touch, and repel each other, while at a slightly (but not much) larger distance there is a slight attraction, the van der Waals attraction, responsible for the formation of liquids.
Thus touching is real. The nuclei don't touch each other but the atoms and molecules do.
Your conclusion is quite unsafe, since your intuition is based on the superseded atomic model of Bohr rather than on modern quantum field theory.