Decorative plants can be potential sources of toxicity. Poinsettias are well known to be toxic, though generally only cause mild signs (mouth and stomach irritation, vomiting). Mistletoe can also be toxic, causing gastrointestinal issues and even cardiovascular collapse. Holly, too, can be highly toxic.
The Christmas tree, whether real or artificial, can also pose risks to pets. Pine needles can puncture your pet's intestines. Ingested ornaments can cause a wide variety of problems, depending on the material the ornament is made from. Cats (and even some dogs) with an inclination to climb the tree could end up pulling the tree down. Even some of the water additives used with real trees can make pets sick.
Electrical cords and lights can be potential sources of electrocution if chewed on by curious pets.
Be sure to keep holiday food out of your pet's reach as well. Candy, cookies, and nuts can all upset your pet's gastrointestinal tract, and some can make your pets incredibly sick. Chocolate can cause a variety of symptoms, including digestive issues, dehydration, excitability, a slow heart rate, seizures, and even death. Macadamia nuts can cause depression, rear limb lameness, vomiting, and tremors. Anything fatty, in general, can lead to pancreatitis. Large amounts of salted nuts can cause sodium toxicosis.
And, finally, tinsel and ribbon. Keep both of these out of reach of your pets. It might seem harmless to let your cat play with tinsel or ribbon, but both can be incredibly dangerous if your cat eats them. Both can easily become life-threatening linear foreign bodies (basically, one end of the linear object anchors somewhere and the rest of it continues to travel through the gastrointestinal tract), wrapping around the intestines and requiring surgery. Think about what happens when you see a loose thread on a blanket, and it sometimes bunches up the material when you pull on it. That's what tinsel and ribbon can do to a pet's intestines. Even worse, the tinsel and ribbon can cut through the intestines. If you have a cat and absolutely insist on using tinsel and ribbon in your decorating, make sure it is completely out of your cat's reach (easier said than done).
There are many more things our pets can get into, so use common sense when decorating for the holidays.