In a world of mountain bikes with dozens of gears, and even internally-geared hubs with 14 speeds, or the Nu-Vinci hubs with their "infinite" gearing (a bit of a misnomer, really), the old 3 Speed can seem hopelessly out of date. Yet, I would have to say that for most average terrain, it is still a superb solution to the gearing question.
The Shimano Nexus 3 Speed set up on my Raleigh Classic Roadster is every inch a no-frills workhorse. It doesn't draw attention to itself and simply does what it is meant to do. In low gear, one can get up some very steep grades. 2nd gear is great for starting off from a dead stop or going up a slight hill/heading into a light wind. High gear is my main cruising gear. At times, it might be nice to have a slightly higher gear for really rolling along (this could be effected by getting a smaller rear cog), but on a utility bike one just doesn't tend to go all that fast anyway, so it really is not something I wish for too much.
When I had an 8 speed Shimano Nexus hub, I found that I really tended to use three gears most of the time, anyway: a low gear, a middle gear, and a high gear. This is true for derailleur setups having 18 or more speeds, as well. While having a three speed takes away some options (and certainly is not appropriate to all situations), it effectively allows for what I tend to do most of the time, anyway--with a hub that weighs considerably less than one with many more speeds.
Three speed gearing systems are very simple to work with. They require a minimum of maintenance (actually, almost none in the case of this Shimano hub), and only the occasional easily-made adjustment. They are excellent for in-town cycling, as you can change gears while stopped as well as when pedaling. The paucity of choices means that I don't actually have to think strategically about gears very much...it is just "L-N-H" (Low, Normal, or High) in my mind, and I can easily pre-plan.
Oddly enough, one of the bonuses to this sort of gearing is auditory. When coasting, the Shimano hub has the familiar sound of pawls rapidly clicking as the hub rotates; but when pedaling it makes the most attractive mechanical susurration...a sort of liquid purring that I find perfectly delightful, rather like the soughing of the reeds down by the river. I never thought I would enjoy the sound of pedaling a bicycle so much!
As a Christian and a priest, I find the number 3 very appropriate and meaningful...it lends a mystical quality to my cycling. I hope that others will come to realize the practicality and the benefits of the old three speed system in today's utility bike.