Antillian bumble-puppies are an adorable life-form native to the Autobot colony world Antilla. Autobots are apparently very fond of them.
Mini Mayhem comics
Jazz reminds Bumblebee that no matter how cool the Fallen may seem, he once shot down a ship filled with Antillian bumble-puppies, and that means he's not an appropriate role model. 
The profile for Thunderblast remarks that Autobots would rather shoot at Antillian bumble-puppies than at a female.
The presence of bumble-puppies in Transformers fiction is an homage to Aldous Huxley's novel "Brave New World," where the creatures were used by social engineers to properly condition (and brainwash) children.