LJ Juggler is an extension for Google's Chrome browser which makes it easy to switch between accounts.

IMPORTANT UPDATE (June 6, 2014): Google has disabled Chrome extensions that aren't installed through the Chrome store. Unfortunately, due to the way Chrome stores data for security purposes, there is no way to transfer data from a non-Chrome store install to a Chrome-store install. I know this is hugely inconvenient, but I haven't found any way to manage a transfer. If anyone knows of a way to access disabled extension data, please let me know. Anyway, all download links should now point to LJ Juggler's home on the Chrome webstore. If you see any that are pointing to the wrong location, let me know!

It's still in the early stages, so there's a little list of things you should know about it.

IMPORTANT! You need to be logged out of LJ when you use LJ Juggler for the first time. This is because it doesn't know how to figure out what your current login is, so it can't switch away from it. After that first time, LJ Juggler will remember who you last logged in as, so this problem goes away.
Not true anymore. LJ Juggler is much smarter than it used to be!

Also worth noting! When you use LJ Juggler it will expire all your existing LJ sessions. This means that any other browsers which are logged in with that account will be logged out. So if you use Firefox and LJlogin, or just log in with a different browser (or from a different machine) sometimes, you'll need to log in again. Sorry it's a pain, but currently there is no simple work-around in Chrome for technical reasons.
Also not true anymore! The 2.0 version of LJ Juggler pretty much fixed all of the really ugly caveats on this page, and most of it came about due to the fact that Chrome has finally main-streamed their cookie manipulating APIs. I probably should have updated it weeks ago.

Special thanks to the LJlogin project. While I didn't end up reusing any of their (generously open-sourced) code, looking through their functions helped me figure out enough about LJ's authentication systems to get this up and running. Thanks bunches!