Well the R group can have basically anything on it. And it is the interaction on these side groups which constitutes the tertiary structure of a protein.
Something which will only have dispersion will be non-polar; I'd say a methyl group.
Another kind of bonding is covalent; this can be di-sulfide, for example, where two S-H groups combine to form an S-S link. There are probably other kinds of covalent bonding possible between side chains, but this is the only example I can think of presently.
There's also Hydrogen bonding. Which could be between carbonyl groups(C=O) and hydroxyl groups(O-H) or Amine groups(N-H2)
Finally(I think) there can be ionic interaction. This happens between a negatively charged species and a positively charged one. A possible combination could be the deprotonated carboxyl group(COO-) and the cationic amine group(NH3+).
I think that is basically it.