So I've got half a spool of new 600V 8/3 Buss Drop Cable, good for 40Amps. What can it be used for? Welder leads? Home made Jumper Cables? Machine cords? It is a flexible and rugged cable meant to be abused. It has 3 wires. Can I use for single phase?
Welder leads? Nope, really not enough ampacity there for 'most' welding. #8 AWG copper is not 'big' enough for most welding, except maybe some low-amp stuff (remember, the 'rated' ampacity there is just 40 amps, and that's on 120 or 240 V with the heating and voltage-drop allowable on those voltages, welding is running much-much lower arc voltages so the % voltage drop comparge to 120V or 240V powerline voltages is much greater.)
Most of the welders I know of or have looked at/up have leads that start at #4 AWG copper, btw. And those are the low-amp low duty-cycle ones with 'short' leads.
Same rationale for using it as jumper cables, Nope. Too much voltage drop % on the lower DC voltage for 12V or 24V high-amp (jumper cable) usage.
Unless you have a need for the buss drop cable, I'd probably suggest to sell or trade it and get what you want or need. Anything else (besides a buss drop

) is using it in a semi (or completely) makeshift manner.
http://www.southwire.com/products/BusDropCable.htm
http://www.southwire.com/products/blackNonULWeldingCable.htm
YMMV.
re: number of phases The wire really doesn't 'care' about the number of phases being conducted as long as the number and size of the conductors and the insulation are 'proper' for the task at hand.