I have used phone wire as a temporary solution (way better than silence). 30W amp/preamp low to medium volume, so I got by. Also I probably wasn't missing much from the entry level system at the time (1986)

I have gone to the bigger wire over ascetics stage, just personal choice, 12AWG, running 200 wpc. I am interested in doing an A/B by doubling the wires to half inductance and see how it sounds. Same would apply to any size wires. Would be an interesting test at 24AWG also. I am running only 6 feet of wire so not sure what gains I would get.

Efficient speakers will help. With 96db speakers, 3 watts may be all you need depending on your preferred listening volume and distance from the speakers.

+1 for 10 watts estimated for 24AWG wire by Cakyol. This provides some margin I am comfortable with for normal use.

If you want to use Erik's 0.577 amp number (good margin) then

I=SQRT(P/R)=SQRT(2.5 watt/8 ohm) = 0.56 amps, so 2.5 watts is no problem. If you are going to run the wire under the rug, over the heat register, or you may have to prove safe design in court even if someone repeatedly set furniture on the wires, then use this number (Seriously, more margin for non standard applications).

Per AWG chart,

https://en.wikipedia.org/wiki/American_wire_gauge
2.1 amps max for 60C rated insulation.

3.5 amps max for 75C rated insulation.

The wire will not melt at this point but any higher temperature, and accelerated heat aging will occur. Reducing life and possibly shorting out eventually. 30+ watts and the risk is higher for early wire insulation failure.

I=SQRT(P/R)=SQRT(30 watt/6 ohm)= 2.24 amps, this is over the rating for 60C wire, this is okay for 75C wire by spec. but not enough margin for me and I don't like my wires hot to the touch. Of course even higher wattage/amperage can result in faster failure by softening or melting the wires.

22AWG phone wire is also available.

Some of the chains stores now offer copper clad aluminum speaker wire, so know what you are getting if you go that route. You will need thicker wire to equal resistance of pure copper 99%+.

Per vassils link, I think the paragraph refers to the 18 AWG wire (0.5M). The 24 AWG is only suggested for digital interconnects.

Some interesting articles linked by others.