Historically, Perl regular expressions were not capable of matching balanced text. As of more recent versions of perl including 5.6.1 experimental features have been added that make it possible to do this. Look at the documentation for the (??{ }) construct in recent perlre manual pages to see an example of matching balanced parentheses. Be sure to take special notice of the warnings present in the manual before making use of this feature.
CPAN contains many modules that can be useful for matching text depending on the context. Damian Conway provides some useful patterns in Regexp::Common. The module Text::Balanced provides a general solution to this problem.
One of the common applications of balanced text matching is working with XML and HTML. There are many modules available that support these needs. Two examples are HTML::Parser and XML::Parser. There are many others.
An elaborate subroutine (for 7-bit ASCII only) to pull out balanced and possibly nested single chars, like ` and ', { and }, or ( and ) can be found in http://www.cpan.org/authors/id/TOMC/scripts/pull_quotes.gz .
The C::Scan module from CPAN also contains such subs for internal use, but they are undocumented.