Cosmic Variance is thankful for the spin-statistics theorem, because it enables the division between matter and force, which is kind of important.
In this spirit, I am thankful for the second Borel-Cantelli lemma, which states that if countably many events E1, E2, E3, ... are independent and the sum of the probabilities of the En diverges to infinity, then the probability that infinitely many of them occur is 1. Let these events be "something interesting happens at time n", for a suitable quantization of time; then given infinite time, infinitely many interesting things will happen. (Of course I'm making an independence assumption here.) I like interesting things.
I am also thankful for whoever it was that took a picture of a monkey at a typewriter.