Do you capitilize the word goth?
I would treat it like the name of any other subculture: punk, hippie, skater, gangsta, and so on. If there were a subculture whose name began with a proper noun--say, "Elizabethan cyberpunk" (that'd be pretty cool, actually!)--then I'd capitalize the proper noun part ("Elizabethan"). But not otherwise.
I'm not sure why this is the case, because other value systems such as religions and political groups--which are also, in a sense, subcultures--get capital letters: Catholic, Jewish, Pagan, Democrat, Green, etc. But for whatever reason, we don't capitalize "punk" or "hippy," and therefore we shouldn't capitalize "goth." I think the confusion with "goth" comes from the fact that you often see "Gothic" capitalized--when you're talking about something that actually is Gothic (e.g. Gothic architecture), I guess it is a proper noun. But not when it's the name of a subculture.