Which can be further broken down.
If we're talking about permanent magnet alternators, a fried ground wire is usually caused by one of two things.
[list type=decimal]
[*]Too much resistance caused by a substandard connection (e.g. corrosion in the wire or terminals, loose connections, etc)
[*]Decreased power consumption by the motorcycle - Removing lights (or turning off lights on a bike that is used to having them on all the time) or swapping out to LEDs will cause the motorcycle to require less electricity. The excess electricity has to be shunted to ground, and that might be more than the wiring or R/R can handle in its stock form.
[/list]
If your problem is the first item on the list, then cutting the wires, stripping them back to bare copper, and replacing the terminals is usually the way to go. A new R/R is sometimes, but not always, needed. www.vintageconnections.com for all your wiring needs.
The second one is a little trickier. You'll still need to replace the bad terminals, but you'll almost definitely need a new regulator/rectifier and sometimes additional wiring to help handle the current. For instance, an upgrade to a MOSFET regulator/rectifier is advised: http://www.sparckmoto.com/Products/Detail/103
I would run a second ground wire as well.