Turning off the engine at stop lights may work OK with petrol engines in warm climates but here in the UK where temperatures are colder and more people drive diesels it can cause problems.
The amp draw required to restart a big diesel engine even when warm is significant due to far higher compression ratio. Constant use of the starter can lead to flat or damaged battery and damaged starters.
The vehicles here that are fitted with stop/start are often fitted with uprated starters, larger or even twin batteries and run lower compression diesels. For example BMW have 16:1 compression in their latest diesels compared with 20:1 or even 22:1 compression ratio on older diesels like my own. Even then there have been numerous issues reported with failures of the systems.
Also if your vehicle is used mostly for longer journeys (extra urban/rural/motorway) the additional weight of the stop/start systems larger batteries combined with less torque at lower rpm can actually lower your overall mpg. So it is not something that works for everybody.
Even though you do not press the gas peddle, the ECM automatically richens the mixture to restart the engine. Most ECM have a lookup table that looks up the coolant temp and air temp to come up with an increased pulse width to richen it up for starting. There is also an afterstart enrichment and a decay setting to control how long the enrichment lasts. Direct injected cars would need the least amount of startup and afterstart enrichment. It's not much, but I don't think it's worth shutting off unless you're going to sit more than 3 or 4 minutes.
Shutting off the engine has the side effect of shutting off the heater or air conditioner. Depending on outside weather conditions, this might be unpleasant. If the car has automatic headlights, shutting off the engine probably also turns off the lights.