This is the inverse of Is there any software which will set the EXIF Dates based on the file's modification date?, and I'm sure all of the programs listed there will apply.

jhead

Of these, for this very simple task, jhead is my suggestion. For example, the command

jhead -ft *.jpg

sets a bunch of files so that the file timestamp matches EXIF.

jhead with find, for going through subdirectories

In order to perform recursion into subdirectories, you could to combine it with the find command available on Linux/Unix/Mac (or Cygwin for Windows):

find . -name '*.jpg' -exec jhead -ft {} +

Or to find any of *.JPG *.JPEG *.jpg *.jpeg ... you can also try

find . -iname '*.jp*g' -exec jhead -ft {} +

You can also use find to just show all the files that would be... found, without executing any other command (like jhead):

find . -iname '*.jp*g'

Other Tools

Other utilities like ExifTool or Exiv2 are much more capable, but at the price of complexity. I can never remember offhand the right options to do anything with those and have to look at the documentation every time, but jhead -ft is easy to remember with the mnemonic "fix time".

ExifTool

Just for completeness, though, I did look at the documentation, and with ExifTool, do this:

exiftool -r '-DateTimeOriginal>FileModifyDate' directoryname

(Remove the -r if you don't want recursion, and if you do that, you can also give a list of files or a wildcard instead of directoryname.) And be careful with those quotes — if you're running this on Windows, you want " instead of '.

Exiv2

With Exiv2:

exiv2 -T rename *.jpg

Beware that with lowercase -t (or without any -T) Exiv2 will also rename the file to a new name based on the timestamp, which may be very confusing. Exiv2 also does not do recursion.