Are there any hostels in Iran?

The main difference between a hotel and a hostel is that a hostel has dorm rooms (exclusively, or in addition to private rooms).

I spent a month in Iran in May 2014 and I did stay in some dorm rooms in Yadz, Shiraz and Isfahan. Still those places felt more like hotels as the majority of the rooms were private and they didn't have a kitchen for guests. Still most of these places were actually really nice and much better than the cheap hotels I stayed at in other towns and it was easy to meet other travelers.

So (as of May 2014), no there are no real backpackers in Iran, but some nice hotels with cheap dorm beds. In most towns you have to stay in hotels. You could also try couch-surfing. It is also possible that some local invite you to stay with them.

Homestay is more common in Iran. Stayed in one in Mashhad, rather by accident, than by choice :) It was not too bad. Don't expect too much. It had hot water, toilet and fan. Location was central, and Valid is able to help you with the visa if you'd like. We later found out, that it is refered in Lonely Planet. Therefore you get to meet foreigners as well. So we had one dutch guy travelling by bike to Thailand. http://www.lonelyplanet.com/iran/northeastern-iran/mashhad/hotels/vali-s-non-smoking-homestay