Can I use 24 gauge speaker cable?

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.

same difference as watering your lawn with a straw or a hose

As is normal here you get a range of answers from zero to infinity, especially on this topic.  My #1 rule is always “Follow your ears”, even to the extent of having regular hearing tests. I mean if your hearing is way off, it is not worth throwing money at. I hear differences between speaker wires an opt for “the low end of the hi end” and am generally quite satisfied.  New old stock can be a tremendous value. 
The older I get, the less it matters in terms hearing loss with age. 

This question is often turned into nonsense.  The technology is really pretty simple to grasp.  If we start with your CD player that has RCA plugs and wire connections we find smaller gauge wires than for speakers.  Quality wire is more important than size because there is 'no resistance' from your amplifier.  A signal is sent a few short feet and the receptical welcomes and all but sucks the signal into the amp.  The speaker wires are leaving the amp and when they cover the distance resistance from the wire itself, it hits the drivers which are all about 'resistance'.  This is where we turn up the amps and the watts to push the signal into drivers and power the drivers.  This is where I use 10 and 12 gauge  speaker wire to transport the full signal and without inhibition that small wires would cause.  Turn up the volume and a 22 gauge wire will fill up and back up and not be able to transport the full signal or to provide the power to drive the speakers.  Remember to think of speakers as 'motors' that require fuel to run.

Hint:  I build my own speakers and I also use the large speaker wires internal to the speaker to carry the signal.  Open up the common commercial speakers and you will find the tiny wires are most common inside the box.  Now a 10 gauge running full out comes to the connection with a tiny internal wire.  The little wire crams the force into this inadequate receptical.  Big wires on the speaker cables will give you the best and fullest signal.  I have used a 22 gauge solid wire of 999.99% pure silver for a tweeter and that can be pretty sweet, but a tweeter rarely calls for more signal because it is only about 10% of total speaker output and a 12" woofer would thrive with a full wire to feed it the 'sounds'.

In short, big wires carry more signal (watts,etx.) to your speakers and mids, woofers and subwoofers perform much better with a large feed wire.

See Roger Rusell a history of speaker wire at Roger-Rusell.com