I see your rant and I raise you a Tom Christiansen contributionTom Christiansen contribution. :-}
I'll take a little license and interpret your question to mean, "Please name some examples where regexes are natural and appropriate."
Small jobs, and in particular one-off jobs, are underappreciated, it seems to me. Suppose that you have one file to parse (maybe you are screen scraping, or maybe you have a data dump from last year and you need to extract the sixth column if it does not start with "%" or "#"). I use a lot of regexes for that.
Another example of small jobs are URL changers, such as in the config file format for Apache (one of many examples here), or Django's urls.py.