I wouldn't consider giving used to stuff to anyone as gifts. This kind of action would seem to be somewhat tacky in my view. I would give used stuff to persons if they really find it useful but when it comes to giving gifts used stuff is completely out of the question.
Well, of course, you should never give your threadbare or nearly threadbare clothes as a gift. That's pretty much disrespectful and can turn people off in a blink of an eye. However, If it's about the things that never grow old... sure, you can. For example, I gave my friend a copy of one of his fav music albums. He knew I owned it. But he's just not into buying physical stuff when it comes to music. It's safe to say he was pretty happy to get the album, as he likes it so much.
As a gift for an occasion? I don't think that will be taken in good stead here because tradition says that gifts should be valuable and new. However, if you give as gift for no occasion, that used item will be appreciated. When we bought a new air conditioner, our old one was still working pretty good and it was there by the doorway, waiting for someone to claim. When my sister dropped by for a visit, she thought we were joking that we would give it away. She was surely glad to take that old air conditioner. Now, that new one was old enough, gave us more than 20 years. The scenario was the same. We bought a new air conditioner and the old one was in the backyard. When our laundry woman asked, she couldn't believe that we were selling it for 10 pesos, that's just a few cents. That's the story of our 2 old air conditioners.
Some people can be finicky, ungrateful, and judgmental, so I think that unless you know the person really well, then you should be careful in giving used items as gifts, since you can get annoyed by their reactions, hehe. They will think of you as a cheapskate! Only do that if the item still looks good as new or it still has a tag on it and it was just not able to be used.
I think this really depends on the person you are giving the gift to. I typically make something new if I am trying to be frugal; however, I have friends who love nothing more than getting cheap, used, thrifted items, and so thrift stores is where I shop. I wouldn't do this for all of my friends and family though, as I have some that prefer new items for the obvious reasons. I'm all about "it's the thought that counts" so I would be happy if someone gave me a box of broken and half missing crayons. My mom always told me that I was too humble, but I'm happy with what I have.