What I miss the most about regexes (and I think is kind of what bermanoid was hinting at) is that we don't have access to much of the expressiveness we usually have available in a programming language. For example, I never saw a widely used regex library that takes advantage of the algebraic structure of regular expressions and that would let me do things like incrementally building regexes or creating named constants:

    var regex1 = /some_regex/,
        regex2 = /other_regex/;

    var regex3 = alternative(regex1, regex2);
    var regex4 = kleene_star( sequence(regex1, regex2) );