Out of interest, what are some of these? I have a hard time believing that the implementors of the Perl regex engine chose to write it that way for no reason while the Thompson NFA figures are thrown about. I knew there must havevbeen something this 'implementation detail' was good for.

An easy example is matching palindromes. You simply can't match a palindrome by moving forward only; you have to go back and see if every letter matches. So, if you want to search for the longest palindrome in a string, you'll necessarily be doing a lot of backtracking.

There's no RE2-compatible regular expression for matching palindromes, but additional features as found in PCRE and similar "regex" engines can do it with backreferences or with look-around assertions. See http://stackoverflow.com/q/3746487 and http://stackoverflow.com/q/3664881 for two ways to write such a regex.

I believe backreferences require backtracking.

No, but variable size lookahead/behind do. This is because the engine has to go back if the remaining part of a regex fails. For some examples, see http://www.regular-expressions.info/recursebacktrack.html)

EDIT: you are correct, backreferences do require backtracking, my bad.