I view networking as a leadership tool in a couple of different ways. First, I think it is part of the leader's role to network. Through networking the leader promotes the organization he or she represents, in addition to developing relationships that can be of benefit to organization and the leader. The larger the network, the larger a pool of resources or potential resources the leader has access to. If a position becomes open the leader might know who could best bring onto to the team to fill it. Or if the leader runs into some type of problem, they might know someone to turn to for advice. For these reasons I think it is the leader's responsibility to network. My thought is that people we consider leaders naturally do this, hence one of the reasons others know them and follow their lead.
An interesting point was brought up in class about social networks on the internet. Those who choose to participate in social networking via the internet are either directly or indirectly representing the organization. This can become an issue if the participant is behaving questionably in a public online domain. This seems like a tricky situation as it is borderline business/personal life - and how far do you take it? But, for myself, I have to think of it in terms of if I owned the company, and this person was behaving in a way that I feel was impacting the business negatively; I would have do something about it. However, the point was also made that before hiring someone it is a good idea to check these networks for these individuals. And I would have to agree with this completely. If a potential hiree posts something for the world to see; it's fair game. And I think you should look to see if it exists or not.
Lastly, I think personally for the leader it is a good idea to network. You want to keep your options open, and never close any doors on yourself (thanks for that one Mom!). Should the company be downsized, the leader would have a healthy network of people to help him or her find another job. Also, there's a chance that you could find a wonderful opportunity through someone in your network - something you might not have heard about otherwise.
So I think, network socially, network for your business -- just network!
LinkedIn http://www.linkedin.com/ gives you a place to start building your business contacts online. I just started mine last week. My dad sent me a link to do this a couple years ago, and I kind of ignored it. After taking a second look, it seems like a good tool and a good idea (Sorry Dad!).