Gum is a running gag in Calvin and Hobbes. Calvin enjoys reading Chewing Magazine, and elevates gum chewing to the status of a sport. Gum was mostly featured in later strips that followed 5/4 through 5/8 1992's introduction of Chewing.
Calvin has also been known to collect bubble gum cards. In one daily strip, Calvin asks Susie if she would like to trade Captain Napalm bubble gum cards, to which she retorts that she doesn't collect Captain Napalm bubble gum cards. Calvin later reflects that "it must be depressing to go through life with no purpose", implying that he thinks the purpose of life is to collect such cards.
Main article: Chewing Magazine (Chewing is categorized as a separate running gag)
Gum chewing magazines were introduced alongside Chewing in the 5/4 through 5/8 1992 story arc. When Hobbes expressed disbelief for the existence of a gum chewing magazine, Calvin replied that had to be a dozen such publications, each marketed to a different class of gum chewers.
Calvin named two of them: Gum Action, which he said "aimed for the gonzo chewers", and Chewers Illustrated, which he claimed was targeted at collectors of vintage gum.
The Gum commercial
Calvin's favorite gum commercial is only referenced once. While Calvin was watching the television at a late hour, his mom come's to put him to bed. He then references it saying "Look, I'll just watch a few more commercials, ok? See, here's my favorite Gum commercial!".