Remember the part about networking? If you're doing it right, you’ll be meeting lots and lots of people in person. Carrying copies of your resume is a little too forward, and do you really want to rely on someone typing your multi-syllable email address into their smartphone accurately as you shout it into their ear while at a loud party?
Create a business card for yourself, and make it a good one. There are plenty of great sites out there, such as vistaprint.com, overnightprints.com, and Moo Cards. Best of all, the prices start at FREE. But once again, you get what you pay for. Sure, you can have a basic white card with black text with your name, email, and phone that doesn't cost you a thing. But for just a bit more, you can get a full-color, 2-sided, glossy card on thicker stock that will leave an impression.
Put it this way -- even if you spent $400 on design and $100 on production to print up 1,000 business cards that said "web developer for hire" and the FIRST card you handed out resulted in a job paying $50,000, would you be upset over the money spent and 999 cards you needed to throw away? I didn’t think so.