What is the advantage to downshifting as you slow down?

Downshifting to a lower gear allows you to use the compression of the engine to assist in slowing the vehicle without wearing down the brakes. This is important on a long downhill where excessive use of the brakes can lead to overheating and brake failure. Downshifting also provides for quicker and smoother acceleration out of a turn or at the end of the downhill.

Downshifting helps slow the car, saving the brakes, but increases wear on the clutch (If you have one). With automatics, downshifting saves brakes and doesn't hurt the transmission.

Now, think about this: A skilled driver driving a manual, can downshift without added wear on the clutch by bringing the engine speed up close to the vehicle speed before letting out the clutch.

You maintain control of the car better. You never know if you will need to speed up.

Down shifting saves wear on the brakes and also is a safety issue. When you downshift you're ready to accelerate if need be.

What others have said, I usually keep the clutch in but move the shifter to the correct gear to match the slowing speed so if for some reason I need to accelerate fast (someone not stopping behind me ) all I have to do is drop the clutch and accelerate.

It will slow you down faster, but wears the clutch more.