This video does a great job of summarizing some of the most common pet gifts that can actually be dangerous. While the squeaky toy caution may be a bit overstated, most of these tips are spot on. With our Golden Retriever, we personally experienced the dangers of rawhide and random objects he ingested. After not one but two exploratory surgeries, we learned to take certain precautions.
Every Christmas, we treated our Fletcher to a 3-foot-long rawhide bone. He would share it with his best friend when she was around, and would gnaw it obsessively every second it was within his reach. Moderation was definitely the key to making this a safe treat. We had to remember to hide the rawhide (see what I did there?) after a few minutes, before he ingested enough to create an intestinal blockage. If you're short on time, it might be a better idea to skip the rawhide entirely, as the vet in this video advises.
For our Golden Retriever, rawhide was the tamest of objects ingested at our house. More interesting items included a diaper (only wet, thankfully) and a blister-type pill pack. The diaper required a half-day of observation and induced vomiting at the vet's office and the pill pack required a very expensive surgery. Thankfully, we had pet insurance and almost all of our vet bills were reimbursed.
My advice is to skip the vet this year with some safety-conscious shopping for your furry friends.