How to undo the last commit in git, but keep my changes as unstaged?

This sounds like a job for git reset --soft, whose help (git help reset) says this:

--soft
    Does not touch the index file nor the working tree at all
    (but resets the head to <commit>, just like all modes do).
    This leaves all your changed files "Changes to be
    committed", as git status would put it.

So the commit is undone, but the files still look the way they did before. Nothing is staged to the index.

I would leave off the --soft in the other two answers and go with a simple git reset @^ (or git reset HEAD^ in older versions of git), which will default to git reset --mixed @^. The difference is that a soft reset leaves the files staged for commit, which is not what it sounds like you want to do. If you really want to undo the commit, you should also probably unstage the changes, which is what the default does. I find this much more useful in the general case than a soft reset, which is probably why mixed is the default.