RULE #1: Friendship trumps acquaintanceship. Business contacts are only as valuable as the depth of connection that you've made. It's one thing to "know of" somebody and quite another thing to actually KNOW somebody. This doesn't mean that you have to be Best Friends For Life with every contact, but it does mean being more than just some dude on their LinkedIn list.
RULE #2: You must be truly worthy of trust. It's a truism that business relationship are built upon trust. In the business world, that trust is not based on how you present yourself, or whether you have common interests, but whether you can be trusted to do what you say you're going to do. That way, your contacts will have no hesitation recommending you to their business contacts!
RULE #3: Regular contact is absolutely necessary. Make a list of the people in your network and schedule some form of contact at regular intervals. Regular contact helps you keep track of what's going on in their lives, and gives you an opportunity to help them achieve their goals, even if you only end up as a sounding post. Regular emails are a good idea, too, but only if they're NOT self-promoting.
RULE #4: You must anticipate your contacts' needs. If a relationship is important to you, you will be proactive about the needs of that relationship. Anticipate what your contacts likely to want and need in their own businesses and careers. Keep an eye out for information and opportunities that might interest them. Help them build out their own network, too. It's time well spent.
RULE #5: Never pass up an opportunity to network. Whenever you're in the same physical vicinity, figure out how to spend "quality" time with your contacts. Needless to say, conferences and seminars are a great place to do this, but any business travel is an opportunity to to meet up with your contacts in that area. Even calling from the local airport to say "hello" shows people you care about them.
RULE #6: Win business for your contacts. There is no faster way to build a solid business relationship than bringing in some clients for the other party. If the contact wins the business or makes some money due to your help, it's a perfect reason to celebrate, in-person if possible. Trust me, such occasions forge business relationships that stand the test of time.
The above is loosely based upon a conversation with sales uber-guru Jeff Gitomer.
Before leaving this subject matter, I simply must tell a story about Rule #5. About a decade ago, I traveled to Bejing to speak at a conference. While I was there, the Chinese translator of one of my books (The Tao of Programming) made a point to call me at the hotel to make sure I was all right and to offer his assistance if I was having any problem.
Here's the thing: he lived on Hainan Island, which is about as far away from Bejing as Los Angeles is from New York. Still, he felt it was important to call and I've never forgotten it, as evidenced by the fact that I'm blogging about it right now. Later on, he asked me to give his daughter her "English" name, which was a great honor.
The truth of the matter is that, after that kind of treatment, I would do almost anything for the guy. He doesn't need my help (he's a big real estate developer in Shanghai now), but all he would need to do is ask, and I'd pretty much do whatever I could to help him out. That's the kind of contact that's worth it's weight in platinum.