There are all sorts of opinions out there on this one, and thus no simple answer. First, it will depend on the fish. Some fish are less active, and easily stressed in large spaces, while others are much more active and prone to behavioral concerns like tailbiting when kept in a smaller container. No matter the size of the tank/bowl, keeping it clean and warm is very important. Filtration and heating are harder in containers smaller than two gallons (though it can work with the right equipment). Really, water quality, heat, and quality of care are far more important to a betta's health than the exact size of the tank. If you keep up with water changes and provide a heater (as well as plenty of decorations for cover and mental stimulation), a betta could do fine in a 2g bowl. In many cases, though, the same betta will do just as well, if not better, in a larger tank, so long as the quality of care is just as good. That probably didn't answer your question at all, but it at least illuminated some of the issues surrounding it.
Like 7103 said, it really depends on the space and the fish. One of my boys is in a 2.5 tank, and really is happier in smaller spaces. The others are in 5 gallons each, but have also lived in 2.5 tanks and don't seem to care either way. But some bettas will get stressed and tail bite in a small environment.