What I carry depends on the dive I am going to do.
I ALWAYS have enough gas to get to the surface if I lose all of mine -- my buddy is carrying it. We know how much it needs to be, and I carry his; we respect those limits.
I always dive with a compass. For shore dives, it's awfully nice to know which way the shore lies. For boat dives, it's nice to know what the outbound course was, in case you get separated from your group (or in our case, because we don't have guided dives in Puget Sound).
For boat dives, I carry mechanisms for signaling a boat. How much and which depends on where we are diving. I always carry a surface marker buoy and spool. If we are never far from a shore where I can exit, that may be all I carry. If I'm more worried about getting separated from the boat, I carry a DiveAlert and a mirror. If we're way the heck in the middle of nowhere, as we were in the Socorros, I carry a Nautilus Lifeline.
You will rarely find me in the water anywhere without some kind of light, unless it is forbidden. If I have a light, I have a backup light, because lights underwater just plain fail sometimes.
I have a knife on my belt. I often have wetnotes to write on, in case we have to have some kind of discussion underwater that can't be managed with hand signals.
I don't carry a lot of stuff. Plan your dives and sites carefully, and select your boat captains well, and you can obviate the necessity for a lot of extras.