How can I keep songs unchecked? I share an iTunes library on another computer in my house. If I uncheck songs so they don't play when I shuffle, the next time I share that library the songs are checked again. No one else re-checked them. How do I keep them unchecked?
when you share a library with another computer, you are not sharing prefenences, just the files.

So when you check/uncheck files you are doing this for teh duration itunes is sharing, as soon as iTunes stops sharing the library, the computer will "forget it" and its settings. 

When it is shared again it will see a new fresh library.