Many hotels will accept a cash deposit ($100-$250 in my experience). The problem is that most often they will say they don't if you call in advance to ask but may say yes if you are asking in person instead. Their official policy is no but if the person is in front of them and seems trustworthy, then they often make a judgement call and accept a cash deposit. But some hotels also categorically refuse whether you ask in person or over the phone. That's the annoying part - there's no real way of knowing until you show up and ask. And that's true for 2* hotels like for 4* hotels (I don't think I've tried at a 5* - there aren't very many of them around anyway! haha)
For obvious reasons, most hotels would not want to advertise that. From my experience, it's possible to find hotels who will accept cash but I'm a sweet and innocent girl who probably looks trustworthy

so that probably helps a little.. although I did always travel with my large dog and that could have been seen as a risk of possible damage. But in the end, I was able to find many hotels that let me give a cash deposit. Must have been my smile. haha Actually, lots of hotels employees were totally in love with my dog and she makes friends everywhere, so she probably helped more than anything else. (She's awesome and very few could resist her

)
I've also used a pre-paid and most hotels at the time (2-3 years ago) had no problem accepting it. (Whole different story for car rentals: they don't accept it and don't make exceptions) I only had 1 hotel say anything about it but I was still able to convince them to accept it. That's it, everyone else just accept it as they would accept any credit card. (For some reason I had issues with cab drivers on more than one occasion - they don't seem to like the prepaid cards.)