From wikipedia:
"The cave stores unique memorabilia items collected from the various cases Batman has worked. Originally, these were stored in a room designed just for them; it was explained that Batman and Robin took one memento from each case. Later, the trophies were shown to be in the large main area of the cave, residing among the rest of the Batcave's furnishings.
The most famous and prevalently featured are a full-size animatronic Tyrannosaurus Rex, a giant Lincoln penny, and an oversized Joker playing card. The T. Rex comes from an adventure on "Dinosaur Island" (Batman #35, 1946); the penny was originally a trophy from Batman's encounter with a penny-obsessed villain named the Penny Plunderer (World's Finest Comics #30, 1947). Other "keepsakes" in the cave come from "The Thousand and One Trophies of Batman!" (Detective Comics #158, 1950). These three stories were reprinted in Batman #256."
