Tire levers are always required. Normally smaller plastic but because I use a more heavy duty tire I carry these metal levers. The longer length allows more torque to be applied when prying of stubborn tires from the rim.
Shock pump for when the forks need some air. As having one's fork bottom out easily is no fun.
Spare tube as it's easier to simply replace the tube and patch the damaged tube at home.
Small hand pump for when a flat happens. In some situations this will be supplemented with a couple CO2 canisters.
Gerber Multi Plier.. handy for many things from pulling objects from tire to cutting up energy bars.
You know it always amazes me how many people ride with nothing for tools. Nothing messes up your ride like having a mechanical that can't be fixed because you don't have tools. Plus in some places it can equal a very miserable walk home.