Clearly the only man here with wife experience. Everyone else suggesting I'm an asshole destined for divorce court... You guys haven't lived with a woman have you?
I'm married and I have experience of hoarders of varying extents. I don't recall seeing anything on this thread that I totally disagree with.
Someone commented with a strategy of "buy one thing, throw two things out", I think it's a nice idea but it would require a mutual honest agreement that you both have everything you need already (and not say a mumbling bit of kind-of-assent but actually discontent which could be a desire to avert another argument).
Throw her stuff out without permission at your own risk. Seriously.
I've also seen situations where the person with the hoarding issue says/acts like that the other person has too much stuff. Combine that with throwing her stuff out, and she might want to take revenge, for example.
In case people think I'm reflecting my own problems here, no, I'm the kind of person who likes the idea that all of one's personal possessions can fit in say a car and just leave

I've stopped buying physical books and only ebooks simply because a) we don't have enough space and b) they're a waste of space IMPO.
Hoarding is something that everyone (I'm pretty sure) does to some extent. I personally go buy the idea of "if I haven't used it in a year, it's not useful enough to keep" (with the generally acceptable exception of say a shopping bag's worth of purely personal, memory-type possessions). My weak spot in this area is my Amiga stuff. I have two (A500 and A1200), both boxed, I haven't started either in at least a year, so really I should sell them, but I'm worried that it might feel as bad as it did when I sold my electric guitar (my logic being, I don't use it really and I'll sell it to someone who makes better use of it), I realised that it was actually a very personal item. It is silly that I would have developed such an attachment to something that I never made much use of in the first place, but there it is.
As I understand it, hoarding is an issue attached to identifying value to material objects. For example, keeping a useful size empty and sturdy cardboard box might be a good idea, however, do you have room for it without losing ease of access to other things? When is it realistic to keep several empty cardboard boxes and why?
My mum keeps packaging bags like the sort that rice is sold in here in the UK, however she uses them up as quickly as she stores them (with my initial assistance she had several spare to begin with), however if someone starts keeping these bags "just in case", then "just a few more", then fails to see the need to review the stock of a "just in case" item (or keeps thinking up more "just in case" scenarios to justify hoarding them), then something has gone wrong somewhere. With people who should be classed as "hoarders", they've developed a personal attachment/value to these items (or perhaps their pride in their foresight to keep something they might need?), and that's when a relationship can go very wrong when someone else comes along and throws "personal" stuff out.