Update Feb. 2021, eleven years later: the new git maintenance command (man page) should supersede git gc, and can be scheduled.
Original: git gc --aggressive is one way to force the prune process to take place (to be sure: git gc --aggressive --prune=now). You have other commands to clean the repo too. Don't forget though, sometimes git gc alone can increase the size of the repo!
It can be also used after a filter-branch, to mark some directories to be removed from the history (with a further gain of space); see here. But that means nobody is pulling from your public repo. filter-branch can keep backup refs in .git/refs/original, so that directory can be cleaned too.
Finally, as mentioned in this comment and this question; cleaning the reflog can help:
git reflog expire --all --expire=now
git gc --prune=now --aggressive
An even more complete, and possibly dangerous, solution is to remove unused objects from a git repository
Note that git filter-repo now (Git 2.24+, Q4 2019) replaces the obsolete git filter-branch or BFG: it is a python-based tool, to be installed first.
Joe suggests:
# Find the largest files in .git:
git rev-list --objects --all | grep -f <(git verify-pack -v .git/objects/pack/*.idx| sort -k 3 -n | cut -f 1 -d " " | tail -10)
# Strat filtering these large files:
git filter-repo --path-glob '../../src/../..' --invert-paths --force
#or
git filter-repo --path-glob '*.zip' --invert-paths --force
#or
git filter-repo --path-glob '*.a' --invert-paths --force
git remote add origin git@github.com:.../...git
git push --all --force
git push --tags --force