You didn't build relationships with your professional contacts just because you wanted people to party with. You did it because they might help you in your career at some point. But the way you ask for that help can kill the relationship. Here's what not to do.
Don't ask too much.
The surest way to get refused or ignored is to ask for so much time and effort, even your best friend would think twice about it. If you're job hunting, request a referral to a specific company, not to have your hand held throughout the entire process.
Don't ask at the last minute.
Nobody is obligated to drop their own agenda to take care of yours. Want an invitation to a networking event? Ask at least a month in advance. The bigger the favor, the more lead time you should allow.
Don't expect them to do all the work.
Before asking someone to help you write your resume, make sure they understand that you've already put a lot of research and planning into it.
Don't ask too soon in the relationship.
Chatting with someone at one conference does not qualify them as a contact you can hit up for career support. A good rule of thumb is that you've known this person for at least a year and had at least four or five conversations (in person, on the phone or online) during that year.
Don't wear out your welcome.
Asking for help once in a while is fine. But don't make people sick of you with constant requests for career advice, project help or employer introductions. Even close contacts that you see every week should not be tapped more than three or four times a year.
One last thing to remember: networking is a two-way street. Return the favor whenever you receive one, or you can be sure that sooner or later that well will run dry.