Originally operating out of the old barn on the Wayne property, Batman accidentally discovered the caverns beneath. At first it was used to store his crimefighting equipment and vehicles, but soon it would serve as his base of operations.
As the Dynamic Duo's crusade continued, more space would be needed. In the diagram shown, which is only a partial view, you can see that Batman began adding a second level.
As the Batman's vehicle fleet and arsenal began to expand, new areas of the cave were opened up, including an underground river/pier to house the batboat and the building of a new hangar in the mountainside cliffs to store Batman's aerial fleet, which were previously stored underneath the barn.
With Dick Grayson off to college, Bruce Wayne decided to move his base of operations to the center of Gotham City. Living in the penthouse of the Wayne Foundation building, Batman moved the contents of the Batcave into a secret sub-basement-turned-cave which became his headquarters for a decade.
Eventually, the base and all of its equipment would be moved back to Wayne Manor when Batman relocated back to the Batcave.
Following the Infinite Crisis, the Wayne Foundation Building was retconned away. Instead, the Wayne Tower would replace it's location, with the Bat Bunker becoming the cave that lay beneath the building, while the building's physical traits would be passed on to the R.H. Kane Building.
In the 80's the Batcave contained the world's most sophisticated computerized crime-lab, an exhaustive computerized file on all known criminals and their methods of operation, a complex workshop where the Batman continues to improve and update the contents of his utility belt, an automotive repair shop, and appropriate housing for his Batmobile, Batplane and Batboat.
At various times Wayne has also used an elevator to reach the Batcave, but has apparently abandoned it due to mechanical difficulties.
The Batcave of the 1990's had a crime lab and forensics tools that rivaled those of the F.B.I. or Interpol. WayneTech sub-contracts ahd advanced the sciences of genetic and fiber analysis, while quantum leaps in computer engineering provided Batman with the hardware and software necessary to assemble the world's foremost digital database on criminals and their psychology. Later on a subway rocket terminal was added thanks to Jean-Paul Valley's stint as Batman, providing Jean-Paul with a fast way to access down-town Gotham other than the Batmobile. Another unique addition to the cave was the handy-man hunchback Harold who was employed by Batman to work in the cave after being saved from Penguin.
Due to increased air-space surveillance by the authorities Batman was forced to ground his flying fleet and rely instead on "borrowed" WayneTech aircraft operating from Gotham hangers. The cave, like the manor above it, fell victim to the earthquake that devastated Gotham. This forced the Dark Knight to remodel drastically.
Completly restructured after the quake and No Man's Land this new Batcave contains 8-levels completly filled with equipment due to a new chasm within the cave. Retractable walkways bridge across the chasm as well as an "island" computer platform with seven linked Cray T932 mainframes and state-of-the-art hologram projector.
Maintained by solar and hydrogen power generators (S-L5) the new cave possesses guest quarters for Batman's allies (S-L1), and an improved gymnasium and shooting range (S-L2). As before Harold lived in the cave (S-L4) before his encounter with Hush, maintaining the vehicles and equipment including the Subway Rocket and Batboat (S-L6). Elevator access is provided to all levels, including a submerged chamber whos purpose is known only to Batman (S-L7).
After the Infinte Crisis occured, many things in the universe were reshaped. The Batcave was no exception with the appearance of the last two batcaves fusing resulting in a cave of collossal proportions both in width and depth. The manor above also received some changes, alternating back to its original design before the quake and No Man's Land era.
This cave would fall victim to Dr Hurt's attack on Batman and his associates, resulting in its destruction, however it was gradually rebuilt thanks to the efforts of the Bat Family.
After the Final Crisis and Bruce Wayne's "death" at the hands of Darkseid, Richard Grayson would eventually take up the mantle of Batman and, in a bid for a fresh start, move the cave back to the abandoned bunker underneath Wayne Tower. However, while Batman (Richard Grayson) and Robin (Damien Wayne) operated from the Bat Bunker, Oracle and Batgirl (Stephanie Brown) would move in and start operating from the original cave under Wayne Manor until Grayson evicted them.
The cave remained empty until Bruce Wayne's return at the apex of a showdown between Grayson and Thomas Wayne (Black Glove), whereapon he restored the cave to operational status and enacted the worldwide, Batman Incorporated, scheme.