Halo currents generated during unmitigated tokamak disruptions are known to develop rotating asymmetric features that are of great concern to ITER because they can dynamically amplify the mechanical stresses on the machine. This paper presents a multi-machine analysis of these phenomena. More specifically, data from C-Mod, NSTX, ASDEX Upgrade, DIII-D, and JET are used to develop empirical scalings of three key quantities: (1) the machine-specific minimum current quench time, tau(CQ); (2) the halo current rotation duration, trot; and (3) the average halo current rotation frequency, < f(h)>. These data reveal that the normalized rotation duration, t(rot)/tau(CQ), and the average rotation velocity, < v(h)>, are surprisingly consistent from machine to machine. Furthermore, comparisons between carbon and metal wall machines show that metal walls have minimal impact on the behavior of rotating halo currents. Finally, upon projecting to ITER, the empirical scalings indicate that substantial halo current rotation above < f(h)> = 20 Hz is to be expected. More importantly, depending on the projected value of tau(CQ) in ITER, substantial rotation could also occur in the resonant frequency range of 6-20 Hz. As such, the possibility of damaging halo current rotation during unmitigated disruptions in ITER cannot be ruled out.