Is it possible to trigger Nikon SB-600 with.. say any flash? If not, what speedlights are capable of this?
EDIT: what's the feature name for googling more details?
Take a look into triggering the Nikon SB-600 using the optical slave mode, or using it in conjunction with an optical slave trigger. It isn't exactly rock solid in the performance area but is very widely supported.
The SB-600 does not offer a 'dumb' optical slave trigger mode, only CLS/AWLS. So you'd be better off getting another flash that uses CLS unless you have reason not to. Don't forget that most Nikon bodies will act as a CLS master via the built in flash though.
You'd require a separate trigger as mentioned by dpollitt's answer.