Cells are keep together by means of a process called "cell adhesion". Single cells have special molecules in their surface that act as glue among them. These molecules are of three types called cell adhesion molecules (CAMs), substrate adhesion molecules (SAMs) and cell junctional molecules (CJMs). All these molecules help cells to stay together without falling apart. For more information read "Topobiology: an introduction to molecular embryology" by Gerald M. Edelman (Basisc Books, NY 1988). Dr. Octavio MiramontesMexico City
There is also the extracellular matrix (ECM) which is made up of glycosaminoglycans (protein sugar)and proteins such as collagen. This ECM acts as a frame work for cells to interact and bind with. ECM is particularly important in bone, cartilage and organs.
The cells actually are wondering the same thing about their constituent molecules, seeing as how the space between the matter dwarfs the actual molecular size. As such they huddle together in groups, in hopes to solve this mystery by combining their collective reasoning.
Well for the constituent molecules, their held together, by their intermolecular bonds, hydrogen bonds and (i think) electrostatic forces between different charged parts of the molecule.Of course the molecules themselves are held together by covalent bonds, bonds created by sharing electrons between atoms.