I had started out putting downloaded patterns in sheet protectors in binders, but it got to be too much. I just keep them as PDFs now. But I still have trouble finding the one I want on my computer.
Paper patterns, I keep in a chest with drawers the size of a pattern, also keep sewing patterns in there.
Patterns in books and magazines, I tend to keep the book or magazine intact, but sometimes I have scanned the pattern so that I have it electronically.