Never give a pet as a gift. Animals are not toys. They require love and attention and a lifetime of proper care, and it is unfair to both the animal and the gift recipient to foist that responsibility on them unawares. If you have already discussed the idea with the prospective recipient at length, and know that they have the time, willingness, ability, and resources to properly care for an animal and make that serious commitment, consider offering them a gift certificate from the local animal shelter (never a pet store!) and going with them to adopt their new companion.
Repeat and re-gifted gifts. There's some leeway here, of course, and as a rule, it's a good idea to keep track of what you give people from year to year, so as not to be continually giving the same type of gift to a particular recipient (show some imagination!). And re-gifting isn't always a bad idea, as long as it's in brand new condition and something you would have bought a particular recipient anyways. But by far the most important thing to avoid is re-gifting a received gift to the original giver. Big no-no. They will remember.
Useless gadgets created just for the holidays. You know the type...the heated car window scraper...the portable mustache trimmer...the bathtub glow light that changes the water's color...i.e. pre-wrapped department store issue, completely superfluous items that the recipient neither wants nor needs, nor will ever use or find anyone else who will use it for them. If you need quick, cheap and easy, go for a box of fancy nuts or chocolates, a department store gift card or the perennial favorite, a bottle of wine.