Yes, they have had multiple themes over the years. Their first theme was this (used in "The Moonbase" and "The Tomb of the Cybermen", although it was a stock music piece and not composed specifically for the show). Here is their second theme, and first original one (used in "Revenge of the Cybermen"). Here is the '80s one, used from "Earthshock"-"Silver Nemesis". For the revived series, the Cybus Cybermen had this theme (from "Rise of the Cybermen"-"Nightmare in Silver") and when some heavily redesigned Mondasians returned in "Nightmare in Silver", this was their theme (changed to this one from "Dark Water" onwards).
So that's six different themes (five for Mondasian, one for Cybus)!