Right click anywhere on the tool bar, and select "Customize..." from the pop-up menu.
Instead, right click on the "Change Connection" icon (), and a customise menu will appear, specific to this icon.
To assign an ALT shortcut key combination to this icon you need to do 2 things:
1. change the position of the & in the "Name:" section - whichever letter the & is immediately before will become the shortcut key you use.
Note that some keys may already be assigned (e.g. ALT-H opens the Help menu, and C opens the Community menu) - but you could change those in the same way.
2. you must select the "Image and Text" option
Now hit close on the "Customize" window that I told you to ignore earlier, and give it a try.
In the example above, this has now set ALT-G to bring up the change connection window - which gives:
Job done - you can thank me later!
UPDATE FOR SQL 2012 - THANKS TO CHADWICK
In SQL 2012, you can access this option via the Customize Menu.
Right click on the menu banner, and select "Customize"
Click on the "Commands" tab.
Click on the radio button next to "Toolbar", then scroll through the list to select "SQL Editor"
Now you can click on the "Change Connection" control, Once highlighted, click on "Modify Selection" over on the right, and set it to "Image and Text", and place the & symbol infront of whatever ALT-KEY you want.