My whole family is re-gift-alicious and we make it fun. There's this football-shaped cheese dip warmer that's been getting passed around in the extended family for probably close to 10 years now - at this point it's almost considered a "prize" to get to be the one who stores it for the year until it's time to wrap it up and stick it under the tree again! Everybody laughs and cheers when someone unwraps that darn thing, LOL. It's still new in the box, technically!
My mom is very poor so her gifts are always either things she had around the house or inexpensive things that she's picked up at a thrift shop, usually along with home-baked cookies. It would be silly for her to go out and buy something for me considering I help her out each month and send extra money ahead of the holiday so she CAN buy some things for my niece and nephew. Some of the gifts she's given me are things that belonged to me as a child - those are some of my favorite gifts.
To me, it really IS the thought that counts, and whether they think of me in a store or if they think of me when they're digging around in their closet or someone's yard sale box that's totally good enough for me. If it's something I don't like or can't use I'll either re-gift or donate it without feeling the least bit of guilt.
I've even given a gift to a cousin and been cheerfully told, "Oh, I already have one of these just like this, I'll give this one to Mom!" and been perfectly happy with that. I gave the gift of them being able to give a gift - they were happy, so I was happy. Works for me!
I probably would be a little bit hurt if something I hand-made especially for someone was given away, but I wouldn't say anything about it. I would probably just think I needed to do a better job at gauging what that person likes because I didn't "nail" it last time. That hasn't happened yet though, to my knowledge.