Vladimir and Estragon are Mr. Ratburn's pet goldfishes. Their first appearance was in Cents-less, where their names were also revealed. They were being fed "breakfast" (fish food) by Mr. Ratburn. Vladimir and Estragon live in Mr. Ratburn's house, in a small fish tank that contains a mini-castle sculpture. They appear again in "Get Smart" and "Lend Me Your Ear".
The names, Vladimir and Estragon, are based on the two main characters from a play called Waiting for Godot by Samuel Beckett. In the play, Vladimir is an intelligent and optimistic character while Estragon is a simplistic character who has a negative outlook on life and humans. Estragon, however, is attached to Vladimir and needs his protection which is why he is seen as more of a child to Vladimir's adult and parent-like character. Since one of Mr. Ratburn's goldfishes is smaller, it can be assumed that he is Estragon, while the larger one is Vladimir.
The fish's tank has no water filter; this could have been seen as an unnecessary detail, or it was forgotten.