Classic style: Manila hemp rope. In executions this is prepared especially by boiling to remove stretch and tendency to coil.
Alternatively: Synthetic fiber rope. Allows a smaller diameter to be used to handle the same amount of weight and have a lower amount of give to them. However, there is then a greater "risk" (or possibility) of decapitation if you're attempting a long drop hanging to break your neck. You might then not be able to use the state execution drop tables.
If you can't get hold of a rope, people have also hanged themselves especially in no and partial suspension with electric cables, towels and so on.
In hangings with no or little drop, I can imagine the type of rope having little importance?
http://www.capitalpunishmentuk.org/hanging2.html#equip
http://www.clarkprosecutor.org/html/death/methods.htm