In general: It depends on load (a value calculated based on RPM, air mass and the volumetric efficiency of the engine), compression ratio of pistons, port vs direct injection, and octane (as well as kind of fuel). Other factors that play a role are ignition and valve timing and transient factors such as air temperature and air pressure. Then there are things to consider such as the temps of exhaust gas and potential for blowback.
For our motor, running everything stock, running a stock tune, and using at least 91 AKI, somewhere between 13.0 and 12.5 is probably around ideal approaching redline, with the leaner value being more forgiving with colder climates, 93 AKI, or higher altitudes (i.e., lower air pressure). Skewing toward the richer value is probably best if running more ignition timing or only minimum recommended octane.
Most engines are tuned to run at or leaner than stoichiometric at idle or light load, which will burn all of the fuel (for petrol, stoich is 14.7:1), optimizing fuel consumption and minimizing harmful exhaust emissions, running incrementally richer as load increases towards redline (afterwhich, the engine is found to dip below peak torque). Peak torque is commonly found to be made (on port injection engines) somewhere around 13.2:1 AFR.
Under high load on our motor, OEM tune plays it uber-safe and has it running rather rich (11.45, going by target AFR) to quench potential hot spots and probably to compensate for an unintentionally sluggish knock sensor response should an idiot consumer fill the tank with any octane petrol below 91 AKI...
On that note, there's a thread on octane requirements every 6 months or so by someone who insists on running low octane fuel in their high performance sports car...
