The vulgar words I'm familiar with all seem to be local slang. Does Spanish have any words that are universally accepted as vulgar or profane?
A vulgarism is a word or custom that degenerates the language, like adding an "s" at the end of the pronouns in the second person "TU" like "comprastes" , "vivistes", "hicistes"
so, long answer short : NO
in the moment a vulgarism is used widely is not a vulgarism anymore, is part of the language.
but if by vulgarism you mean insults, yeah there are plenty.