Generally, I don't chuck any nicely bound course packets because, hey, they were costly. In classes where articles may have collected loosely in folders, I tend to get rid of the articles (or, if they're printed single-sided, recycle them in the printer).
To combat my worry that I may someday want to re-read those articles, or wonder "what was that great piece we read in X class?" I file the syllabi in my filing cabinet. That was something I began doing after my undergraduate years because when I started teaching I was always looking for inspiration, trying to remember how my professors had written their courses.
The point is to keep as little paperwork as possible, but the "possible" part means not throwing anything out that may be of genuine use. I'd love to get rid of some of my course books, but too many of them this quarter are in the "going to an office someday" category to be let go of.
"Someday" being the operative word.