It's crucial to come to an interview well prepared. Of course, that means preparing answers to predictable questions, and dressing so that you look the part. But preparation also means bringing the correct documentation. You'll instantly come across as a professional if you bring additional copies of your resume and recommendation letters.
Why Bring Them
You might think that everyone in the interview will have seen your resume. After all, you used it to apply for the job. But that's not always the case. While the principal interviewer usually has a copy, sometimes you'll be interviewed by a panel, and everyone might not have your resume in front of them. It's also possible that during a long day of interviewing, paper documents have gone astray, and the interviewer might not be able to instantly locate your resume.
When you bring along multiple copies of your resume, you will impress the interview panel with your thoughtfulness and professionalism. If someone on the panel does have a question about your resume, it's very satisfying to be able to offer them a copy. You also may not have had an opportunity during an automated application process to offer letters of recommendation, so your interview can be a good time to let the panel know you have a good reputation in the industry.
Your resume should be printed on heavyweight off-white paper in black ink in a conservative font. If possible, keep it to one page. Every copy should look perfect. Never hand out a resume that's dog-eared, folded or smeared. It's acceptable for good letters to be photocopied, of course, but do it onto quality paper. Have each packet paper-clipped together, with the resume on top and the good letters beneath. You should use a smart, professional-looking briefcase to carry these documents into the interview.
When to Offer
Get your handouts out of the way right at the beginning of the interview. If you do it later, it could interrupt the flow of the meeting. Walk in, shake hands with each interviewer, and as you sit down say "I've brought my resume and some recommendation letters -- would you like a copy?" This way you allow the interviewers to remain in charge -- they can decide whether they need a copy -- but you've given them the opportunity, and you've stressed your preparation and professionalism.