The Simpsons' household pet is a cute but untrained
greyhound. Bart rescued him from a dog racing track. Homer was relying on a Christmas bonus to buy presents, but didn't get it. He took the small amount of Christmas money Marge was saving, with the intention of betting it at the dog track. He had inside information on what dog was going to win, but instead bet on the "long-shot", Santa's Little Helper, believing it to be a sign. Santa's Little Helper lost, and his owner abandoned him. Homer and Bart brought him home, and everyone was so happy with him that it was a merry Christmas after all.
In one episode, Bart trades Santa's Little Helper away for a different, "super-dog" that can do anything by means of credit card fraud. Homer even liked the dog--you can tell by his comment, "a dog like that, you have to feed every day." Of course, they eventually have to go get Santa's Little Helper back.
See: Characters from The Simpsons