Our cats (2) give and get gifts.
They give gifts to our pet sitters (2) cats, cause our pet sitter rocks and any reason for her to want to watch our fur balls is a good reason.
They give gifts to my husband and I, usually things that we get for free or nearly free with coupons (since they are on a limited hair ball budget).
Also each year they receive a large combined gift (examples include a new water fountain, cat tree, etc) and get a stocking full of treats from "Santa-cat".
Sometimes they receive treats and such from other family members, but the cats are re-gift-ers. Those are given those to the shelter (since they have some dietary restrictions).
I nearly forgot their favorite parts of Christmas, wrapping paper balls to play with, one mylar balloon with the ribbon replaced with a cloth ribbon (which is only out when supervised--they love balloons), and their favorite activity is helping to personalize and wrap all the gifts, by chewing on the ribbon or bows.

(We have to put all the wrapped with ribbon gifts in a closet after they get a minute or two to add their touches). The cats are definitely an active part of our household holiday.