How to replace spaces in file names using a bash script

I use:

for f in *\ *; do mv "$f" "${f// /_}"; done

Though it's not recursive, it's quite fast and simple. I'm sure someone here could update it to be recursive.

The ${f// /_} part utilizes bash's parameter expansion mechanism to replace a pattern within a parameter with supplied string. The relevant syntax is ${parameter/pattern/string}. See: https://www.gnu.org/software/bash/manual/html_node/Shell-Parameter-Expansion.html or http://wiki.bash-hackers.org/syntax/pe .

Use rename (aka prename) which is a Perl script which may be on your system already. Do it in two steps:

find . -name "* *" -type d | rename 's/ /_/g'    # do the directories first
find . -name "* *" -type f | rename 's/ /_/g'

Based on Jürgen's answer and able to handle multiple layers of files and directories in a single bound using the "Revision 1.5 1998/12/18 16:16:31 rmb1" version of /usr/bin/rename (a Perl script):

find /tmp/ -depth -name "* *" -execdir rename 's/ /_/g' "{}" \;