What can you bring with you on a submarine?

It depends on how much space you're allowed - NUG's and FLOB's (New Useless Guys and FreeLoading Oxygen Breathers) pretty much get rack space as their limit. If you're hot racking on Port/Starboard watches (12 hrs on/12 hrs off watch instead of the normal 6 on/18 off) with another person (you're sleeping in the rack while your buddy is on watch, then he's in it while you're on watch) then you share rack space, and your total gets halved. NUG's and FLOB's are usually too busy qualifying and studying, so they don't need that much anyway. It's even harder if you're on a longer deployment with riders and they're using portable temporary racks in the Torpedo room (nothing quite like sleeping next to a Mk 48 Torpedo or a Tomahawk missile), since even opening the rack is a real pain.

Cameras are a no-no unless you've got specific permission from the CO. Yes, the pics on my bio page were authorized - I always had a camera with me.

Most people new to submarine duty always take a lot more than they need. You only really need 2 or 3 uniforms and associated clothes, some civvies, media player of some type, reading material, etc. These days boats have DVD / BD players, so they don't have to load a ton of 16mm film movies like we used to for movies. Submariners wear Topsiders or some type of sneaker underway, which is arguably one of the best features of submarine duty.

Rack space is pretty tight - there's only about 4 inches (if that) of depth, and 6' long and 2' wide. The washer and dryer are usually going non-stop on long deployments, so clean stuff isn't a problem. Soap, deodorant, shaving gear and tooth stuff is mandatory, unless you really want to deal with the rest of the crew.

Over time, as you advance in rank and qualifications, you might get more space with lockers (e.g., I had 5 separate lockers for use, as I was the ship's PAO, Engraver, and Deck Division Supervisor) and you can always squeeze personal stuff in there. Back in the days when they didn't have soda machines, I brought a case of Coke with us to the North Pole in one of my lockers. I also lived on board for a few months, and I was allowed some extra space as a result. But I was also a Senior Petty Officer also; when I first came aboard, I didn't get squat for space.

Rule of thumb - pack light as you really don't need that much. If you're not on watch, you're training, eating or sleeping, so there's not much rec time anyway. Each CO will authorize or prohibit certain items as he sees fit (Video Games, etc.), but music players are pretty standard. You don't ever want to get caught screwing around if you're behind on training either, unless you want a world of hurt directed at you. Guys that aren't Qualified in Submarines or aren't at least qualified on their own systems have no business doing rec time when they could be working on qualification.