In general, cables can be run exposed for just about anything. For power and lighting circuits, the exposed cable can not be "subject to physical damage" (true also for flex conduits and sch 40 PVC). Subject to physical damage is not well defined in the code, but is up to the inspector to judge. Often times, once the cable is more than 8' above grade/floor, many will allow it exposed.
The CL2/CL3, CATV, Communications, etc cables don't have the physical damage restriction. Note that running speaker or other low voltage cables in the wall will require that you use listed cables (e.g. a CL2/CL3/CM/CATV label on the cable). If you're just running speaker wires from an amplifier, along the floor and up the wall to a ceiling mounted spaeker, I don't think that falls under the NEC and you can use whatever type of cable you want.