In a car with an automatic transmission, we are normally greeted by the acronym PRNDL, or in some cases (older cars) PRND21.
I know that the L, 1, or 2 will cause the transmission to stay in a (L)ow gear and not upshift, but I've heard various explanations of what the low gears are for. I've only used them to play around with, and never felt like I had a reason to use them. It's the automatic's job to pick the correct gear, right?
By setting L (or 1 or 2), the gear will stay low and you will be able to use engine brake, instead of using brakes all the way down the hill and suffering from fading. The transmission will not necessarily pick a lower gear when going downhill, although they will pick a low gear if you are going uphill.
Never brake the car for an extended time when going downhill. This can be a life or death decision, specially if you are crossing a mountain pass. If you use the brakes for a extended time, besides needing to maintain them more often, you may risk having no brakes after a while. Truck drivers should always do that and often there are sign on the side of the highways remembering to do that. Usually those signs read "Use low gear". For trucks that don't do that or that suffered a brake failure for other reasons, there are escape ramps filled with sand or other material to reduce the speed of runaway trucks.
I personally always use L whenever is safe to do so in order to save fuel and the brake pads. It is a habit that I kept since I started driving (in a stick shift).
Two additional uses alongside engine braking controlling downhill descents:
If you need to go up a steep hill on loose terrain like a sandy dirty track, dune or fine gravel, you need to build up momentum before hitting the incline and you need to put your foot down and get high revs for the speed you're travelling at. Leaving an automatic on D risks it going up a gear too quickly, having insufficient power and losing momentum on encountering the incline leaving you in stuck with wheel spin. Fixing the gear in 1 or L lets you put your foot down and get the high revs necessary.
I lost a tire in a remote African village attempting a dusty sandy hill in D then losing momentum like this. After changing wheel with some help from the villagers, then rolling all the way down to flat ground, I hit it in L with foot firmly down and cruised over the hill like it wasn't there.
From Land Rover's off road driving guide:
Deep mud or sand needs a steady momentum to carry you through ... in sand, the lower gear the better.
Too much power when driving in icy conditions or wet mud will simply cause the wheels to slip, so you might want to put the gear in to 2nd and then drive with low revs. In D, it might drop down a gear and you'd have too much power.
From Land Rover again:
In mud, too low a gear causes wheel spin.
Stay in a higher gear for better control, and if it is slippery, in a manual car move off in a higher gear, rather than just using first.
In very bad conditions, crawling along in 2nd (and possibly even starting in second, depending on how the particular automatic transmission adapts) might be necessary.
The only time I've ever felt the need to use anything other than 'D' in an automatic is when towing or climbing a steep grade. That's not to say I don't play around like it's a stick shift sometimes, but as you said, it's not necessary.
The other day, I had to pull a damaged car (one wheel was locked up) across an apt complex. I put the tow car in 1 in order to keep the torque and speed up, instead of allowing it to shift into second and dropping the engine out of the power band.
Similarly, when climbing a steep highway grade in an under-powered 4 cylinder car, I left it in 3, because it kept wanting to shift into 4th, then it wouldn't have enough torque to hold 70 mph, so I'd have my foot to the floor and it would downshift into 3rd to get the speed back, and so on and so forth.
Edit: gabrieldiego's answer reminded me I do that too, having gotten so used to driving manual transmissions. Because the torque converter is not a direct link to the engine, however, it doesn't slow you down nearly as much as engine braking with a manual transmission.
While the others has stated why you might want to use one of the lower gears, they aren't explaining what happens when you actually use the lower gears.
On most vehicles with automatic transmissions, when you put the vehicle into "2", the transmission goes into second gear. You don't start in first gear, then shift up to second, it starts in 2nd gear. This reduces the amount of torque going to the wheels, which may help in situations where you want to reduce wheel spin, such as when stuck in the mud/snow. Having the wheels turn slower actually helps in this situation, as spinning most of the times will just get you stuck worse.
