I find myself having to apply the break pedal everytime I go down an inclination. It's not too steep but the car seems to gain speed faster and faster.
In the other cars I have driven, this was not the case. cars would maintain their speed without much change even without holding the break pedal.
At risk of sounding facetious, yes it is normal. It's due to gravity. The steeper the slope the greater the acceleration.
Exceptions include: some off road vehicles which use intelligent engine braking for downhill, but even they will only cope up to a certain slope angle, loss of grip.
It could be the gear ratios in your car. Vehicles that are geared lower will hold their speed going down hills using the concepts of engine braking, while vehicles geared really high will be more likely to gain speed as a result of little to no engine braking.
The other cause could be your idle setting. If your car is set to idle really high, it's going to take off on it's own, without pressing the accelerator.
This very much depends on the incline.
If it is a slight incline, I would expect that the vehicle would still accelerate, but probably not if you are going fast (Over 30 mph, say). If it's more than a 5 degree incline, then you could probably go highway speeds without touching the gas.
If you find yourself riding the break, as has been suggested, try going into a lower gear, even in an automatic. That should take care of the problem for you, slowing you down without wearing out the brakes.
It could be various reasons, like speed at which you enter the slope. Probably nothing is wrong with your car.