I can totally empathise. I have DVDs and books - no idea how many, but a LOT. Enough to take up all the shelf space in our lounge. And people do the exact same thing to me - they ask to borrow them. I have learnt to refuse. "No, sorry, I don't lend out DVDs."
I mainly learnt my lesson from a friend who, being such a good friend, was always asking to borrow box sets so she and her husband could watch them "when they had time". The thing was, they never had time. They were always at school working, or at their kids' school functions or at church. They would keep my box sets for months and months. I'd ask for them back and Trish would say, "Oh, but I haven't finished watching them. Maybe I'll bring them (sigh) even though I still haven't seen them all." And then she'd say she forgot when I asked again. Finally when I got truly vererg (annoyed) she said, "If you come over to my house you can get them." I had avoided going to her house because she has cats and I'm very allergic and had weaned myself off of the expensive, steroid-based nasal spray and was doing well. Going to her house meant I had to buy allergy medication. Anyway, I did it so I could get my DVDs back. Then later when she asked to borrow more I'd say, "I'll bring them" and thereafter claimed to have forgotten every time she asked. Yes, she eventually stopped asking.
Now I just say I don't lend out DVDs. To anyone, ever.