I had an open suitcase in the nursery from about 36weeks, but it really didn't have anything in it until I was about 38wks pregnant. My waters broke when I was 39w2d pregnant, so just in time
In retrospect, I did a great job of packing things for the birth, but not such a great job of packing things for the hospital stay afterwards. I only packed 1 skirt ... I had nothing else to wear, and no pyjamas, so I had to ask DH to find my trakkie pants (which he couldn't find).