The hostel called 'Auberge Riad Douzi' is located in the middle of the Medina and very close to the Place Jeema El Fna.
It might be a bit difficult to find but it is a great refuge to escape from the huddling people in the city.
As far as I know there are no separate rooms but only dorms with 4, 6 or 8 beds; some of the dorms also have private shower/toilet. In the morning there is a quite small breakfast and of course the sweet Moroccan mint tea.
This hostel is also a good place to get into contact with other travellers :)
During my stay in Morocco I ended up in Marrakech 3 times and always went to this hostel without a reservation - it was always possible to get a room and I even slept on the terrace for EUR 5 as it was cheaper and the air in the rooms can be quite sticky. Usually you can still negotiate the price on the arrival which in the end might be due to not fulfilled reservation requests.
However, the owner of the hostel and the staff is very friendly and welcoming - they can even give you some tips, buy spices or argan oil for you, etc. I recommend to book bus tickets via the owners as it is lots easier than going the whole way to the station to be disappointed there.