JoJo asks about quality. Most of the responses are about pixel accuracy, which is all but irrelevant for a designer, or even a photographer.
Quality is a measure of how convincing and pleasing the end result is, not how "accurate" it is. As a great case in point, Cloning or Content Aware Fill replace unwanted parts of an image with plausible pixels: they look right, but they certainly can't be considered accurate.
In Photoshop, the main practical difference between downsizing incrementally vs. downsizing in one shot is that it takes a lot longer. If you charge by the hour, by all means go 1% at a time. If not, downsize in one shot. Make the image a Smart Object first, in case you ever want to make a bigger version later.
No matter what algorithm you use (and Dawson's comment about those algorithms is dead on -- they are amazing), downsizing throws away pixels. The algorithm subtracts pixels and modifies others by guessing how to make them look right. A good algorithm makes good guesses; it gives you a result that looks convincing, but it's not accurate in any meaningful sense. Honestly, accurate -- other than color! -- is not what you're looking for unless you're a scientist, in which case you probably would not be downsizing in the first place.
An image that's been downsized using the usual bicubic algorithm often benefits from a little bit of sharpening, but if you're creating jpegs for the web, sharpening will increase the file size.
Correct quality in design is the quality you need for your end product. Anything beyond that adds time, but not value, to your work.
[Edit: Since there was a mention of enlarging in koiyu's revival of this question. I've added some comments on that subject.]
There's an idea kicking around that if you up-rez an image in small steps, as opposed to a single giant leap, you get a slightly better ("slightly less bad" would be more accurate) result. Scott Kelby promoted the idea some years ago, and it may have been true as of PS 7. I've not seen anything that convinced me that it's correct today. It didn't prove out in my own tests, back around PS CS2 and 3, but it has to be said that I didn't waste a lot of time on them.
I didn't spend time on deep testing because the slight difference between "degraded image quality" and "slightly less degraded image quality" has no practical value: neither is usable. In my own work, my simple rule is, "Don't upsize." As a matter of practicality in design work, an image that is a bit too low resolution for a particular purpose always looks better used as-is than that same image "up-sized" to the "correct" resolution by any process I've come across, including fractal and bicubic variations.