Also note that tightening might fix it but you must make sure you tension it properly. If you overtighten you risk stuffing the bearings in the alternator and whatever else runs off that belt (water pump, PS, AC compressor etc)

Over time the belts do stretch slightly but they also go hard and shiny. Generally I'd say just replace the belt unless you have good reason not to.

How do you know for sure it's the alternator belt. Some cars have 2 or 3 or even 4 belts for all the accesories. Newer cars tend to have serpentine belt arrangements where basically everything runs off one big belt snaking it's way around.