For OW dives besides the standard equipment (buoyancy, mask, fins, regulator etc.):
A line cutting device or/and EMT shears (on harness waist webbing)
Small torch (on right shoulder webbing)
SMB w/spool (pocket)
For liveaboards I take a few spares just in case I lose or break one (don't necessarily dive with them, besides computer and torch for night dives): mask, fin strap, torch, computer, smb. When I go with whole family I also add one extra bladder (just the inner thingy), one inflator mechanism, one extra fin for all of us. I happened a few times to have a family member lose a fin while climbing to dingy, twice managed to salvage in time, once used the spare replacement.. Computers had also three times where the spare was needed: once someone placed the tank on, another battery died, and one also went overboard or what I call a tribute for Neptune...So spares do come handy sometimes.