I'm surprised that everyone (including the FAQ) missed the most obvious solution which uses an alternation. Most other solutions seem to forget that the $ anchor is right before the trailing newline. :)

$string =~ s/^\s+|\s+$//gm;
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If you want to preserve blank lines, it's a tiny bit longer.

s/^[\t\f ]+|[\t\f ]+$//mg;
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Remember: in Perl, the common things are supposed to be easy, so if you're doing something common and it's not easy, you're probably missing something. :)

I'm going to update the FAQ answer too.