Is it something you get? What about it stresses you? Do you get "infected" by other people's stress?
I myself don't really stress about it as a whole, but there are two things that cause some worry most years.
First is the fact that my mom always stresses about Christmas. Not sure why, but she does, so I try not to get in her way and add to her stress. During Christmas we spend more time together than usually, so the odds of me getting in her way are higher, which is stressing.
Then there's Christmas presents. I tend to just get something little for my closer relatives, but when it comes to my family's gifts, I try to put some thought in to it and get something they'll really like, even giving one or two of them something slightly more valuable. When I do that though, it stresses me even more as I'm never completely sure they'll like it/find it useful. Also, it's hard to come up with ideas of what to give. Mom's always been easy, and my little sister used to be too, but she's growing up now and I still have no idea what to get her this year. Usually the problem is my big sister, but she moved out on her own last year and is still missing one rather essential thing that I can afford and get my hands on, so I'll get her that. Of course, my dad's also a problem every year. I just don't know what he'd like and stuff I get him usually goes unused unless it's chocolate... with clothes there's the problem that I'm not sure about the needed sizes.
And no, I can't just leave someone in the family without a present. That'd be rude when everyone else gets one (or sometimes two, even three when my little sister was small and I couldn't resist buying nice but cheap toys and stuff.)