Basic rooms in a shared flat just a few minutes from the Rambla in an area called Raval (by the youth hostel). You have to phone Leonardo, the guy who rents the rooms, to show you round.
You get your own key so you come and go as you like. Best thing is it has a shared kitchen, so you don't have to eat out all the time. It's all a bit disorganised, but friendly. Don't be put off by the filthy entrance to the building!
They ask 20 euros a night and you can negotiate a discount for longer stays. They even have a web page - http://www.rooms-barcelona.com - if you want to check it out before phoning . . .