You can work out what gauge of wire required using the following formula:
I = sqrt (W/R)
For example, to deliver 100 W into 16 Ohms:
I = sqrt (100/16) = 2.5 A
So you would require a wire rated for 2.5 amps minimum so 16/0.2 (thats 16 strands of 0.2 mm) which is rated at 3A will be fine. I generally use 24/0.2 which is rated at 6 A.
http://www.maplin.co.uk/module.aspx?ITAG=SPEC&ModuleNo=6198&doy=9m11#specObviously it would seem that the thicker the cable the better, however if the cable is too thick it is very difficult to solder to the speaker and jack terminals.
Two further observations. I've NEVER seen speaker cable fail in an amp, even in transistor amps where the output has shorted out. Secondly, have you ever seen the guage of wire used for speaker coils? You might be surprised how small it is!
I don't advise using solid core wire as it can break more easily due to metal fatigue, especially if you are not careful stripping it and you score the wire. I often see broken solid core wires in older amps. I doubt there would be any difference in sound. It is occasionally argued that skin effect makes multicore wire a better conductor at high frequencies so should be more trebly, however this is nonsense as skin effect only starts to become an issue a frequencies well outside the audio range.
Where anyone has cared to investigate in a scientific manner for hi-fi purposes no-one has demonstated any differences in the sounds of cables. See the link below for a good article on this by Douglas Self (someone who does really know what he is talking about).
http://www.dself.dsl.pipex.com/ampins/pseudo/subjectv.htm