I had to think a while to answer this as we don't have traditional...traditions.
My kids would write their wish lists and I told them that if they asked for a sweater, for example, they should donate a sweater to a needy person. Likewise, if they asked for a book or toy, etc. This served two purposes. It made room in the house for the new gifts they would receive, and it taught them to think of others before themselves.
We made and exchanged a lot of homemade gifts when money was tight. All gifts are appreciated as it is always the thought that counts. But I remember one year when we took a pile of mail order catalogs and did something I called "circle down". Each of us would draw a circle around something in the catalog that, if we had the money, we would buy for each other. That was a lot of fun.
Granted, not as much fun as Mimosas for breakfast,
but fun nonetheless.