Bamm-Bamm Rubble is Barney and Betty Rubble's adopted son in the Hanna-Barbera animated television series The Flintstones. During the show's fourth season, Betty and Barney, desperately wished they had a baby like their best friends' child, Pebbles Flintstone, and the next morning, Bamm-Bamm, who had originally been raised by dinosaurs in the wild (according to a Flintstones trading card released in the 1990s), arrived on their doorstep. From the very start, he showed amazing strength and a deep affection for Pebbles, which she reciprocated, both as friend and crush. It is shown in the made-for-TV movies I Yabba-Dabba Do! and Hollyrock-a-Bye Baby that Bamm-Bamm and Pebbles eventually marry and later have two children named Chip and Roxy.
Appearances in Christmas specials
The Flintstones

Bamm-Bamm in A Flintstones' Christmas Carol.
The Christmas specials Bamm-Bamm has appeared in have featured him and Pebbles at various ages, ranging from toddlers to preteens to married parents with their own children. However, Bamm-Bamm's role in the original series' Christmas episode, "Christmas Flintstone", is rather minor. He is seen playing with his adoptive father and their pet Hopparoo, Hoppy, early on in the episode, while Barney tells Betty about Fred getting a part-time job at Macyrock's Department Store. He is not seen again in the episode until the closing scene with the two families celebrating Christmas together.
Chronologically, Bamm-Bamm's next appearance in a Christmas production is the series' fourth Christmas production, A Flintstones' Christmas Carol, which appears to take place shortly after the original series (possibly the year after the events of "Christmas Flintstone"). Bamm-Bamm is now able to say words other than his own name, and he has the part of Tiny Tim in the Bedrock Players' stage production of A Christmas Carol. He ends up getting stage fright when he is supposed to say "God bless us, everyone!" at the very end of the show, so Pebbles ends up saying the line instead. Outside of a few Pebbles Cereal commercials that came later, this movie would notably mark the final major production in which Bamm-Bamm was voiced by his original voice actor, Don Messick, who passed away a few years after its premiere.

Bamm-Bamm at elementary school age, as seen in A Flintstone Christmas.
The second Flintstones Christmas special produced, A Flintstone Christmas, chronologically takes place when Bamm-Bamm and Pebbles are at elementary school age. At the very beginning, Bamm-Bamm and his adoptive mother are shown helping Wilma and Pebbles bring their Christmas tree home. Later, after Fred places a heavy ornament in the wrong spot on the tree and causes it to fall over, Bamm-Bamm lifts the tree up and places it back in its upright position. He and Pebbles are later seen at the Ladies' Auxiliary's party with the other children, becoming impatient in waiting for Santa (Fred) to show up. At the very end of the special, he and Pebbles, along with their respective fathers, are shown waving to Santa when they see him flying in the sky.

The adult Bamm-Bamm helping Stoney put the star on top of the Flintstones' tree.
Finally, in A Flintstone Family Christmas, the only Flintstones Christmas production that takes place after I Yabba-Dabba Do! and Hollyrock-a-Bye Baby, the adult Pebbles and Bamm-Bamm call to say that they and their kids, Chip and Roxy, are flying from Hollyrock to spend Christmas with their families in Bedrock. Midway through the special, however, their flight is delayed by bad weather. Fortunately, by the end of the special, the couple and their children eventually arrive at the Flintstone residence in time to celebrate Christmas with their families, including Pebbles' new adopted brother, Stoney, whom he helps put the star on top of the Flintstones' tree. Though he was voiced by Jerry Houser in the aforementioned made-for-TV movies, Bamm-Bamm oddly does not have an actual speaking part in this special, outside of singing Christmas carols with the others at the end.
Spin-offs
Outside of The Flintstones itself, Bamm-Bamm also starred in "Cave Kid Christmas", the Christmas episode of his and Pebbles' short-lived spin-off, Cave Kids. As the series takes place when the two are preschoolers, this would indicate that "Cave Kid Christmas" comes between A Flintstones' Christmas Carol and A Flintstone Christmas in chronological order.
Bamm-Bamm's most recent appearance in a Christmas special was the Yabba-Dabba Dinosaurs episode "The Spirit of Frostnos".