I use the shortcut w to move the cursor one word right. Is there a shortcut to move a word left?
In addition to the b movement mentionned in the other answers, another movement which may be interesting is ge.
It brings you to the last letter of the word on the left. When b is considered as the opposite of w, ge can be considered as the opposite of e which brings you to the end of the current word.
Also note that all of those word-wise movement have a WORD-wise equivalent: W, B, E and gE which are "faster". For the difference between words and WORDS see: :h word.