DMSO and acetone have almost identical structures, except for us replacing the carbonyl carbon with sulfur to obtain DMSO. DMSO's melting point is 19 °C$19~\mathrm{^\circ C}$, whereas acetone's is -95 °C$-95\ \mathrm{^\circ C}$.
Is the dominant factor DMSO's larger molecular weight? Probably not. While acetone is 58 g/mol$58\ \mathrm{g/mol}$ vs. DMSO's 78 g/mol$78\ \mathrm{g/mol}$, 2-pentanone is 86 g/mol$86\ \mathrm{g/mol}$, but still has a very low melting temperature of -77 °C$-77\ \mathrm{^\circ C}$.
The only protons on all of these species are aliphatic, so hydrogen bonding is probably not the dominant contributor to this effect either.
What's going on?!