I don't like handing over a generic resume; a resume should be tailored to the employer, and should name the employer in the objective line.
Objective: Employment as Head Bottlewasher for Larry's Coca-Cola Recycling Service, Inc.
Objective: Employment as Captain for Ernie's UFO Interplanetary Travel, LLC
Objective: Career Employment with McDonalds Corporation as French Fry Tester.
This means that you need to have researched the companies to whom you intend applying. If you're going to a job fair that lasts a full day, or a couple of days, you may not know who all the employers are when you arrive. In thsi case, you could make a generic resume and cover letter, or you could collect business cards right off the bat, retreat to your hotel or a business center and print out fresh, dedicated resumes. If it were me, and I intended to seriously seek employment, I'd customize each resume and cover letter.
If you collect business cards and names in the morning, or on day one, you can have a cover letter addressed to a specific recruiter when you return...much more impressive.
Some may not want to go this far, but today getting business cards printed is cheap and easy at any office store. Have cards to hand out with your cell and your name and a them regarding your qualifications. Add a slogan, any slogan, and you're set. I like a blank card with only my name, cell, a job description such as "Aviator," or "Fly Swatter," and a little slogan such as "Anytime, Anywhere," (I know, it's been used) or "Here to serve you best." never mind the grammatical imperfections...the point is something, anything, that means when you bring back your current resume, you'll be better remembered.
Knowing the companies in advance is best. If you have a list of the companies that will be attending, do a little research on each one. If you take some notes, and they don't need to be much, you can review them quickly before shaking hands at a booth or seminar. Your information will be fresh in your mind when you meet the recruiter, and you don't need to worry about memorizing a lot of details for the whole assembly, or worse, remembering the wrong information.
Good luck!