For me three-speed hubs are the "Goldilocks" of gears - not too few, but not too many; advanced enough to give a real benefit, without being complicated to maintain.
Far and away the most popular three-speed hub is the Sturmey-Archer AW model.
Produced from 1936 to 2001, in the original form, in a modified (and improved!) form it is still being made today.The three gears are set at 75%, 100%, and 133%, for an overall spread of 1.77x from lowest to highest gear.
This is the setup I use every day.
I start off in first gear (flattish road - slight uphill incline) to warm my legs up a bit, then after that it's into second. I then stay in second for the rest of the incline, then switch into third for the descent that leads to where I work.
Back into first or second when manoeuvring to the bike racks at work, which involves going down a fairly narrow alleyway that leads to the rear of the office.
On the way home, I start in first, and cycle up the alleyway (moderate slope), then up the steeper slope at the end of the front carpark, and out onto the road again. Then it is into second on the cycle path. For the main climb on the way home (not that much of a slope really, I usually use second gear, but if I get stuck behind someone, then I drop to first. When the path levels out a bit, it is into second, then third again. First gear to cross the road at the lights, then second and third the rest of the way home (it is a slight downhill from this point).
That's why I ride a three-speed bike. I use all three of the gears each time I commute to work. Regular maintenance is almost as easy as for a single-speed bike (just got to add a bit of oil to the rear hub every now and then, and check the setting for the gear cable coming out of the hub), and a three-speed is a much easier bike to ride every day than a single-speed (and I am speaking as one who rode a single-speed almost every day for 5 years!).
The chain is also just as easy to enclose as with a single-speed, and a three-speed with a full chaincase makes for a pleasent commuter bike.
As well as several models currently available from Sturmey-Archer, three-speed hubs are also made by Shimano (the Nexus hub) and SRAM (the i-Motion hub).If you wish to thank me for this article, then please comment or click on one of the advertisers' links - you might like some of the cycling related stuff (I know I do!)