Last summer I gave the Square Foot Gardening thing a try and we built 2 beds that are 4' by 4', 6" deep, and 4 1' by 6' beds (also 6" deep). They all worked really well for what I grew even with just 6" of soil. I didn't grow any root vegetables though.
Of course you can always make them deeper if you'd like, but if you can come across one of the books (or just look it up online) there are great ideas for adding things to your raised beds such as a chicken wire cover to keep bunnies & deer out (which we did, and it worked great!), and ideas to make season extenders & trellises & such.