A find -exec answer is a good one but it suffers from the usually irrelevant shortcoming that it creates a separate sub-process for every single file. However it's perfectly functional and will only perform badly when the number of files gets really large. Using xargs will batch up the file names into large groups before running a sub-process for that group of files.
You just have to be careful that, in using xargs, you properly handle filenames with embedded spaces, newlines or other special characters in them.
A solution that solves both these problems is (assuming you have a decent enough find and xargs implementation):
find . -type f -print0 | xargs -0 chmod 644
The -print0 causes find to terminate the file names on its output stream with a NUL character (rather than a space) and the -0 to xargs lets it know that it should expect that as the input format.