I collect programs from all the plays I've seen and worked on. Having these little booklets allows me to have all the information for a play at my fingertips. I have recently been updating my resume and website as I am graduating with my MFA soon and inevitably I forget who designed what. Sometimes as an assistant I never really talk with the lighting designer, for example, so I may not know their names off the top of my head.
Besides having programs for my own shows, I have programs from shows I was an audience member for. (Now, I don't have them from ALL shows as most programs in Europe are not free. They cost money. Granted, each program is only one to two pounds in London, but those add up when you are living abroad on a rather strict budget.) Having the names of designers on shows I haven't worked on is great. If I really liked a show's design I can look up other work by that designer. I use the programs as a way to broaden my designer knowledge.