I'd like to be able to switch between my favorite boards easily.
It's actually much better to use browser tabs to do this.
If we were to allow you to "pin" boards to a navigation bar across the top of the Trello window, we'd have two choices:
Neither of these is a great option, so the best thing to do is use the tabbed browsing functionality already in your browser.
You can even bookmark your favorite boards and put them all in a folder on your browser's bookmarks bar. Then, center-clicking (with the mouse wheel) will open all the tabs at once (in Firefox or Chrome, at least). I made a screencast to demonstrate this here: http://screencast.com/t/BhjtPD2e
That second click is a mouse wheel center-click.
Another quick way to switch boards is to use the 'b' shortcut and search your boards. Press 'b' to open the boards menu in the header and the search box will be automatically focused. Just start typing the name of the board and press enter to jump to it immediately. You can use the up and down arrows to navigate the list.