Between two DMSO molecules, there two intermolecular forces present: London dispersion forces and dipole-dipole forces.
First, London dispersion forces are present in all molecules, polar and nonpolar alike. The force is a force of attraction between any two molecules that forms temporary dipoles which are caused by the movement of electrons around two atoms. One end of a polar molecule can become temporarily positive, while another end can become temporarily negative. These temporary dipoles allow for two DMSO molecules to be attracted to each other.
Second, dipole-dipole forces are present in all polar molecules, which really are dipoles. A dipole-dipole force is an electrostatic attraction caused by the positive end of one dipole being attracted to the negative end of the other dipole. Between two DMSO molecules, the oxygen of one DMSO molecule would be attracted to the hydrogen of the other DMSO molecule. In the diagram below, the dotted line represents the electrostatic force between the two DMSO molecules.
Now, hydrogen bonding is a special case of dipole-dipole attraction, in which a temporary covalent bond forms between the hydrogen of one molecule and the oxygen, nitrogen, or fluorine of an adjacent molecule. In the case of DMSO, hydrogen bonding cannot occur! DMSO is a polar aprotic solvent. An aprotic solvent is a solvent that cannot donate hydrogen. A polar aprotic solvent is an aprotic solvent that lacks an acidic hydrogen. Therefore, hydrogen bonding is not present in DMSO, it being a polar aprotic solvent.