Great question! 1) Molecules and atoms are held together by electronic attraction - electromagnetism. It is usually considered under the heading of chemical bonding, which is explained by electromagnetic interaction. Electrons are held in their orbits about the nucleus of an atom by the same electromagnetic force. Chemical bonds could be viewed as an extension of that force. Quantum electrodynamics is usually the heading under which these interactions are examined. 2) The nucleus of the atom is composed of protons and neutrons (1H being the line exception). Atomic nuclei (and all those protons that don't like each other and electromagnetically repel) are held together by nuclear binding energy, or nuclear glue. It is derived from or could be seen to be an extension of the strong force. This binding energy comes from what is called mass defecit - the affected neutrons and protons (during the fusion process) give up a bit of their mass and it is converted into this binding energy. The quarks and gluons that compose individual neutrons and protons are understood to be kept together by the strong interaction or strong force. It is usually considered under the heading of quantum chromodynamics. 3) Of course gravity hold planets, stars, galaxies and loose stuff together generally. It is the large-scale organizer of the universe. The electromagnetic force and the strong force and gravity are three of the four fundamental forces of the universe. Only the weak force, which mediates types of nuclear decay (beta decay being the primary example), is not represented. Wikipedia has more information, and links are provided.
Gravity..
matter
electromagnetic force
The electromagnetic force holds unlike particles of matter together. In chemistry, that would be positively and negatively charged ions, and the protons and electrons in individual atoms.
Dark matter is all around us, inside and out, is what holds the forces of gravity together, keeps it from flying apart.
It is gravity that holds the universe "together" as we know it. Gravity, and not nuclear forces, are the large scale organizers of matter in our universe.
Solids hold their shape due to their atoms being held tightly together.
Matter attracts each other same as the phenomenon of magnet's unlike and like poles attract and repel each other.
All phases of matter have the strong force. It is the force that occurs in the nuclei of atoms and holds the protons and neutrons together in the nucleus.
the gravitational force holds its atmosphere together
Gravity - from the stars, dust, etc., but especially from "dark matter", a substance of yet unknown composition.
Wood glue holds boards together.