Depends on what your definition of regular speaker wire is.
The primary concern is that you don't overheat the wires. This usually is not much of a concern though, unless you are running some serious speakers at very high power. 200 watts into a 4 ohm speaker would only draw 7 amps through the wires so even 18 awg would survice.
The next issue is power loss due to the resistance of the wire and the increase in overall impedance that it will introduce. Any added resistance due to the wire means that the amp will need to provide a higher output voltage to deliver the same power, and it is often the voltage limits that restrict how much power the amp can put out. It also means that the total power of the amp needs to be more because some will be lost in the wires.
If you have ample head room in the amp ( the amp can drive significantly more power than the speakers will tolerate) then I wouldn't worry about the power lost in the wires and I would recommend 16 awg wire so that running the wires was easier.
I would also recommend using a "tinned" wire so that the copper doesn't corrode as bad.