Rule number one: Don't be overly aggressive. Even if a contact is a potential employer, you can indicate that you are looking for new prospects indirectly without making a direct – and inappropriate – request. Avoid constantly asking for favors and do favors for others whenever possible.
Also, don't go to parties, inter-hospital committee meetings, or Little League games "on the make," quickly sifting the wheat from the chaff (i.e., those who may potentially advance your career from those who are likely useless to your career) and dumping the latter for the former, fawning over them and dispensing business cards in a manner that would make the businessmen in And remember that, while it's important to keep in touch with contacts, calling them every day to see if they've heard of new opportunities will turn them off – calling once a month is fine. Similarly, don't dump them as a friend/contact once you have found your next job.
Finally, since the ideal networking relationship benefits both parties, always think about what you could do to help the other person.