Yes, I reuse them. If they are in good shape, they go to people outside the family. If they are in bad shape, DH gets the next present in them. Hey, I've taped ripped paper together for some of his presents. He doesn't care what they look like as long as we recycle.
I do often reuse gift bags and boxes. There are so many occasions where I receive a gift bag where it is in excellent condition after opening the gift. The same is true for boxes. While I do buy gift bags, boxes, and wrapping paper for special occasions, it is sometimes easier (and a lot more cost effective) to reuse a gift bag or box that someone has recently given me. I draw the line at a bag or box that is torn, has a hole in it, or looks used. But, that rarely is the case.
One thing I do in order to dress up a reused bag or box is to add fresh tissue paper and a decoration of some sort. I find it adds a special touch and makes the reused gift bag or box look fresh and new -- and it makes the individual I'm giving a gift to feel special as well. In my opinion, there is nothing wrong with reusing gift bags or boxes. But, I never reuse wrapping paper! I'm too messy a package opener for that!