You can get extra promotion and visibility mileage out of your giveaway. Tell everyone that you'll be holding a contest over the next 2-3 months. Anyone spotted wearing the bracelet/shirt/hat/ or using the cup/pen/whatever in the library at random, unannounced times, will get a special reward and their names entered into a larger drawing for a larger prize. This gives you several visibility opportunities for announcing the winners, reminding people about the random sightings, and building up for the grand prize drawing.
Another option is to doing the "spotting" in a public venues, like a football game. Then you'll be encouraging everyone to wear something that advertises the library (walking billboards) and the winners can be announced during the half-time on the loudspeaker (free PR broadcast).
So don't just give something away. Make it count towards your overall marketing and communications strategy. It doesn't take much more effort and you'll get a better ROI.
This is a great tip and radio stations do this all the time with great success. Has anyone actually executed this idea? How'd it go?
See the original question about ideas of promotions items to give away at orientations at the Academic PR Forum.