I, too, am in the regift camp. I'm also in agreement that as long as the gift is new and doesn't get given to the xrayperson who gave it, then there is nothing wrong with doing it. Money can be tight and I would rather regift something I couldn't/didn't use to someone who might otherwise not get as much from me. I sent a little embroidered owl that held a hand sanitizer on a key chain, to my dd along with a mini table runner. Both were little gifts from my guild Christmas party. Now I did send her other things that I had bought just for her, but I thought that they were some things she would like. I didn't wrap them just stuck them in the box.
We also have an annual Christmas party at my church and we do a really fun gift exchange. I have regifted items for this and like someone else mentioned, it's encouraged. Lots of fun.