It depends. LEDs come in all different shapes, sizes, and colours. 9V's come in different types, as well. If you have an LED that draws 10 mA and a battery that supplies 500 mAhrs, which would both be somewhere around the middle of the realm of reality, then you should expect approximately 50 hours of use before it goes out. If you use a large or bright LED, as opposed to a small indicator light, that could drop significantly. If you use an old NiCd battery or the battery is powering anything other than the LED, then the life will drop significantly. For example, some old NiCd's only had a capacity of about 150 mAhrs, and a big LED might require as much as 100 mA, then you get an hour and a half of life.
On the other hand, maybe you go with a really efficient, small LED that draws only 6 mA and a beefier lithium 9V that has a capacity of 1200 mAhrs, then you could get 200 hours.
So, anywhere between one hour and maybe upwards of two hundred hours, depending.