Off the top of my head, rope to put down Gide lines in case you get silted out so you have something to follow to get out.
Also extra everything, if your open water diving and you run out of air (or other critial equipment failure) you can roll the dice on the bends by going straight to the surface, not so with cave diving; your just going to drown.
If I'm not wrong so many people got oxygen poisoning in there and got confused with their path where they came in and out then went in deeper instead of going out when the tank almost empty
I'm not a caver or a diver, but I've read a few stories about cave diving. A big one is a cable on a retracting reel. Caves which are frequently explored will have guide cables bolted along the walls for long stretches. You snap your cable onto these and then use it as a leash back to the guide. This allows you to explore off a certain distance without getting lost. You can always follow your own line back to the guide, and follow the guide back out. In an "unimproved" cave, you'd presumably want lots of extra line to build your own guides.