In June, we stayed at OKW, and we received 1 packet of dishwashing detergent. I asked for more, but mousekeeping gave me one more packet. (Of course I asked again, and I got some more.)
I think it depends on how much cooking you plan to do. I usually bring an extra dish towel, and we wash a lot of clothes, so I wash the kitchen towels at the same time. I also bring liquid hand soap to put at the kitchen sink and ziploc bags to store just about anything in.