There are many ways on how you receive traffic.
Direct traffic if your url is already familiar to your customers that they type your link directly on your web browser's address bar. If they already bookmarked your website's url because they already found it useful they want to access it with just one click. The list goes on and on how your website could get traffic.
So why do we expect more traffic from only Google?
Actually, not only are we expecting traffic from Google, but from other Search Engines as well. As replied by others, Yahoo and Bing are also good traffic sources, but Google is undeniably one of the usually used Search Engines. One good indicator of this is how "google" word is now being used as a verb now becoming synonymous to the terms look, and search.
I suppose it also depends on your target customers, where do you suppose will they go to look for answers on their particular need? If the answer is Google, might as well do something to generate more traffic there.