And if push --force doesn't work you can do push --delete. Look at 2^nd line on this instance:

git reset --hard HEAD~3  # reset current branch to 3 commits ago
git push origin master --delete  # do a very very bad bad thing
git push origin master  # regular push

But beware...

Never ever go back on a public git history!

In other words:

• Don't ever force push on a public repository.
• Don't do this or anything that can break someone's pull.
• Don't ever reset or rewrite history in a repo someone might have already pulled.

Of course there are exceptionally rare exceptions even to this rule, but in most cases it's not needed to do it and it will generate problems to everyone else.

Do a revert instead.

And always be careful with what you push to a public repo. Reverting:

git revert -n HEAD~3..HEAD  # prepare a new commit reverting last 3 commits
git commit -m "sorry - revert last 3 commits because I was not careful"
git push origin master  # regular push

In effect, both origin HEADs (from the revert and from the evil reset) will contain the same files.

edit to add updated info and more arguments around push --force

Consider pushing force with lease instead of push, but still prefer revert

Another problem push --force may bring is when someone push anything before you do, but after you've already fetched. If you push force your rebased version now you will replace work from others.

git push --force-with-lease introduced in the git 1.8.5 (thanks to @VonC comment on the question) tries to address this specific issue. Basically, it will bring an error and not push if the remote was modified since your latest fetch.

This is good if you're really sure a push --force is needed, but still want to prevent more problems. I'd go as far to say it should be the default push --force behaviour. But it's still far from being an excuse to force a push. People who fetched before your rebase will still have lots of troubles, which could be easily avoided if you had reverted instead.

And since we're talking about git --push instances...

Why would anyone want to force push?

@linquize brought a good push force example on the comments: sensitive data. You've wrongly leaked data that shouldn't be pushed. If you're fast enough, you can "fix"* it by forcing a push on top.

* The data will still be on the remote unless you also do a garbage collect, or clean it somehow. There is also the obvious potential for it to be spread by others who'd fetched it already, but you get the idea.