drumbent has had good luck with 3 speeds, but he has the advantage of having access to a healthy stock of old parts. Jim hughes above has expressed disappointment in the quaity and durability of 3 speed hubs.
THe disconnect here is the wide range of quality you can find if you look at a population of 3 speed hubs. THere are a few categories we in Canada are likely to encounter:

1. Old Sturmy Archer hubs (~early mid 1970s and older)... these are great... built like farm equipment, remained unchanged for the better part of the 20th century. Serviceable.
2. Middle-aged sturmey archer hubs (late 1970s, 1980s, maybe up to 1990s) - still made in UK but with vastly inferior materials. Less reliable.
3. Old Shimano 3 speeds - an inferior version similar to SA hubs, but quite poor and unreliable
4. New sturmey archer hubs - made in Taiwan, probably better than the middle aged UK ones, but I have no experience with these.
5. New SHimano 3 speed hubs - the Nexus version, which I am led to believe are very good. My Alfine 8 is a 'cousin' of the Nexus 3 speed and it has been fantastic.
6. Others - my wife had a 1970s Fuji with a Suntour copy of a SA-AW hub, but it lost its middle gear after a while. There are Sachs that are likely quite good. And I think few others but they are quite rare.

The first three are the most commonly found on used bikes. The new Shimano ones are found on quite a few new bikes - cruisers and the like.

The one concern I have with Jim Hughes' comments is that his rusted on the inside... before I knew how to do any maintenance on any other bike part, I knew that some rear wheels had an oil port on the hub... a few drops of oil in there every other month should be all the maintenance these need. Maybe this was the problem he had... lack of maintenance?