I have been *desperate* for an extension that would do this for years, and even moreso since upgrading to Joomla 2.5 seems to have stopped the old direct url login method from working.
The extension is well named, as when I logged in to the backend and saw it log in to the front end, I did infact feel like "Wow! I have what I need at last! Woo Hoo!". Unfortunately there was just one small thing missing... specifically that when you log *out* of the backend that it doesn't log you out of the fron end, too. It only works for logging *in*. That said, there is a workaround... just click the "log user out" button next to your username on the Joomla control panel before logging out.
That said, this plugin performs a critical feature that I've been wanting for years for free no less, so I am *extremely* grateful it exists. Now, if you get it logging out of the frontend, too, it'll be absolutely perfect.