I've released an imaginatively-named utility which I've been using for years to set image file modification times using the EXIF headers. I've looked at several other similar tools but this one adds some error handling and uses the Perl Image::Exif module (which means it can handle non-JPEG formats including my camera's Olympus RAW).
The only dependency (Image::Exif) can be easily satisfied: on Debian or Ubuntu installing
sudo apt-get install libimage-exif-perl); on systems like Mac OS X which lack an APT-equivalent:
sudo -H cpan Image::Exif