The problem is when you try to do something like use regular expressions to match HTML. If you know the least bit of formal grammar theory, you'll know how maladapted that is.
Lua is interesting in that instead of using traditional regex it comes with its own "pattern" matching - the implementation is much cleaner than most regex implementations. See http://www.lua.org/pil/20.1.html for a bit more info.
I reply to this comment because Lua patterns actually have an operator to match balanced parentheses (or any pair of characters): %b()
Also worth a look if you're feeling bored of regex are PEGs, which leads me nicely onto: http://www.inf.puc-rio.br/~roberto/lpeg/lpeg.html
(and finally yes, everything I do or speak about does tend to revolve around Lua)
The entire Regexp::Common namespace is basically a cookbook of the "right" way to use regular expressions. Worth stealing and porting to other languages...