Shortcut for maximising IE windows is the same as maximising any other window.
Press Alt+Space to get the window menu, then press X to maximise the window. Once you've pressed Alt+Space, you can also use other shortcuts: R restores them to non-maximized mode and N minimises, for example.
Not sure if this is super useful if you've got 60 windows to maximise, but it's faster than finding the maximize button and clicking it individually 60 times..
On a side note, a handy trick if you ever lose a window (e.g. it's offscreen) is the following: Press Alt+Space for window menu, press M to start moving the window, press any arrow key to make the mouse cursor jump to the title bar of the window, and then move the mouse around wildly to get the window back on screen :)
Edit: Ampersand's answer is simpler for anyone on Windows 7 or above.