TL;DR Both Auschwitz camps are open for individual tourists. No reservations can be made, and buildings are closed and routes shortened. It is still worth visiting the camps.
Due to the excellent answer by Andrew, I took the gamble and travelled to Oswiecim (Auschwitz). I was actually able to enter both Auschwitz I (the smaller camp near the city) and Auschwitz II-Birkenau (the larger camp outside of the city).
As far as I could judge, the situation is very different from other days. My recommendation for individual visitors, is to go to Auschwitz I first. If you come by car, you can still park close by (although not on the official spots) and it is a short walk from the train station. At this site, all buildings and expositions are closed, and there is only one route possible through the camp. It is however still worth going there. Make sure that you don't bring a back-pack, they are not allowed on the site.
If you exit Auschwitz I, there are free buses leaving on a regular basis to Auschwitz II-Birkenau. At this camp, there is also only one route available. The route is however long and impressive and worth the visit. Note that there is no bus for the reverse route (it is only a short 2 km walk back to the station).
One warning, I went there the 24th of July. This is before the official start of the World Youth Days. I expect that is will get more crowded during the official days, but I guess (disclaimer: I don't know for sure) that individual tourists will not be stopped at the entrance. Note that there is also a day scheduled where the Pope will visit the camps, avoid this day altogether.
Furthermore: at the entrance of Auschwitz I and halfway Auschwitz II-Birkenau, there are small stalls where you can by a bottle of water (4 zl/1€).