Most stuff has been mentioned, but what about O2 kit and first aid kits?
What I carry depends on the dive I am doing but the two things I feel are overlooked by most recreational divers is a spare mask and DSMB.
A spare mask is an essential bit of kit for technical divers but for recreational divers, what do you do in 20 metres of water if you lose your mask? Even with your buddy to guide you, your ascent is going to be uncomfortable. If you are in the sea, diving from a boat and your buddy is less than attentive, can you find the shot?
DSMBs seem to be carried by many UK divers (and those diving in parts of the world with similar conditions) but many don't. In sunnier climes where the sea is clear, they seem to be a rarity. Although you should try to avoid buddy separation, it does happen and a DSMB is useful. When I dive with a new buddy, I make a point of telling them I have one and in the event of separation, it goes up. We do the usual search for no more than a minute and the first on the surface can see the buoy.
If diving from a boat and a shot line isn't used, or you can't find the shot, it makes it easier to be picked up by the boat. It also helps stop you getting run over if for some reason you have to surface somewhere unplanned. It can be used as an additional source of buoyancy and can help you be spotted if you end up adrift. Most skippers in the UK insist divers carry at least one per buddy pair.
