While there are a great many benefits with networking, one of the most beneficial is creating awareness. If your goal is to expand your business and gain market share, awareness is an absolute necessity. You must be top of mind to be in the discussion process for prospective clients. If you aren't in the the equation, you cannot be selected.
Awareness also serves as a benefit when you are looking for a job, needing help with a project, or simply desire to expand your circle of influence. In an economic environment that has a high level of unemployment, there are going to be more people vying for the same jobs. Networking and creating awareness for yourself, will allow you to have more chances to gain employment.

This is something of tremendous benefit that is one of the more commonly left out networking benefits. The ability to gain new knowledge from another person is huge. New ideas can reveal benefits of your existing product or service that you didn't think of. It can be a different perspective on the current marketing angle you are using, or it be a whole new position about what you are doing. 

The ability to gain a new perspective is crucial. Networking provides the opportunity to test market your ideas to people. A third party can be a great benefit as they have nothing personally invested in you. At times, people can be too close to a situation, and they can get blinded by their own "good" ideas. Allow yourself the opportunity to increase your success odds by speaking to others.

When you take the step of advancing your current circle of influence, you vastly increase your chances of having new opportunities offered to you. Opportunities can be for business, pleasure, personal growth, career advancement, or simply just knowledge. One of the worlds greatest business minds, Dale Carnegie, once said, "Smart business people understand the value of networking. Put simply, expanding your contacts improves your chances to build good relationships, discover leads and generate increased sales."

There is no shortage of networking opportunities to take advantage of, especially with the constant expansion of the Internet. Try some of these:
Chamber of Commerce
Toastmasters
Facebook
LinkedIn
Twitter
Tips:
When attending an event in person, try to find out who will be there in advance.
Bring plenty of business cards.
Prepare an interesting 30-second vision that you can present fluently to others.
Be willing to listen and provide value to another person before asking for help.