Repeating some of what's been added above, but some of this depends on your budget and how much time/effort you want to invest in taking video as well as how experienced of a diver you are (worry about task loading).
My $0.02, in priority order (I have a Hero 3+ I've been using for a little over 2 years) -
- Red filter for clear water diving (or magenta/green water for cold/low vis). I use the Backscatter flip system, which is well made and produces great footage
- Tray of some sort to keep the camera stable. 2 handles are better than one for steadier footage. Make sure you have a good lanyard and perhaps some sort of clip as well if you need to clip it to yourself in an emergency
- Micro Memory cards = memory is cheap. Number of memory cards depends on trip logistics. Rather than bringing a laptop or external drive...I bring 1 32 GB card per day of diving on dive trips. Also limits risk of lost footage due to flooding to what you've taken that day
- Agree with the GoPro moisture munchers - I use at least one of these per dive regardless of temp. They are reusable
- Agree with multiple batteries, assuming you want to use it for every dive. The number of batteries depends on how you are using the camera in terms of trip logistics and the ability to charge batteries between dives. For trips where you are doing 5 dives/day, 3-4 batteries might be necessary (I have 4...on certain trips where there are 2 morning boat dives (without returning to the dock), 2 afternoon boat dives and a night dive, 4 are needed in order to keep up with the charging). I change the battery on every dive. For liveaboards where you come back to the mother ship after every dive and can switch-out/charge, 2-3 is probably enough. If using the LCD backpack screen and keeping the camera on for the entire dive, the camera battery tends to last about 1.5 dives for me. Some folks use tricks to extend this (camera off when not shooting, etc.)
- The GoPro multi-battery charger allows you to charge 2 at a time
- The LCD back-pack - critical if you want to see what you're shooting/frame shots. Also easier to see what mode/navigate though settings menu underwater if needed.
- Light(s) = 1 is better than none and 2 are better than 1

. Huge range of prices depending on your budget. Also pay attention to battery question...same issues regarding logistics as the camera batteries. Some lights have removable batteries where you can have more than 1...some have built-in batteries that are not removable...but which may last more than 1 dive depending on how long/bright you burn them on each dive. A great starter tray/light combo is the Sea-Dragon 1200 made by Sea-Life. I used this until I recently upgraded to 2 lights recently
- Macro lens. I use the Macromate mini from Backscatter. The beauty of their flip system is that you can easily switch between wide angle filter and macro lens without any screwing/snapping on/off underwater
- One underrated factor to consider - figure out how you will carry all this stuff on a trip. I have a camera back-pack I use when flying for dive trips...lots of pockets for memory cards, batteries, etc., etc.