Try using find with -exec.
Code:
find /etc -exec stat -c "%a" '{}' \;
If you're using bash version 4 there's also a new ** recursive globbing function. But you have to enable it first.
Code:
shopt -s globstar
stat -c "%a" **
But find has an advantage in that you can use it to fine-tune the types of matches you want, such as using "-type d" to get directory permissions only.