I was checking out a definition on Wiktionary, one of Wikipedia's sister projects, and I logged in to correct a typo.
After logging in, I was taken to the usual "return to the page you were on before logging in" page, but this page also included a link, saying, "To use this account on other Wikimedia wikis visit Special:MergeAccount. I had never heard of it before, but it looked to be something very useful for people like me: a unified login across all WikiMedia projects (including Wiktionary, Wikibooks, Wikimedia Commons, as well as Wikipedias in other languages).
Sure enough, it was. And it was quite a painless procedure, so long as your username and e-mail address are the same across the Wikis (the password does not have to be the same on each Wiki).
Since you have just logged in, you merely have to enter your password on your primary wiki. Since most of my edits are on en:Wikipedia, but I was logged in to en:Wiktionary which had a different password, I entered my Wikipedia password.
It then cross-references the different Wikipedia projects and shows you a list of those on which you have an account that matches the given parameters, and with the click of one last button, you can unify your accounts.
And you're done! If I wanted to log in to a Wikimedia project where I haven't been before, I can now use my Unified login and not have to register from scratch. Now that is a useful feature!
It determines your primary account by looking for which project you have the most edits on (or if you are an Admin or Sysop on one of the projects). You can see which projects you have edits on by entering your username at the User Contributions Tool. I have the most of my edits on en:Wikipedia--613 edits!