An unpleasent fungal infection.
A lot of people mention Athlete's Foot as an argument against people having a shoes-off policy. However, this is a quite unnecessary concern.
Athlete's Foot is generally associated with swimming pools and changing rooms. It is possible to catch Athlete's Foot on one's barefeet at a swimming pool or in a locker room. However, recent research indicates that this is not so likely as was previously thought.
Most importantly, the reason people catch Athlete's Foot in those places is not because people there are barefoot, but because the fungus needs a warm and wet environment. People get exposed to the fungus in the damp conditions. If they fail to dry their feet, the fungus is very comfortable and even more so if the victim puts on sweaty socks.
The fungus will not survive long on the clean, dry floor or carpet of a person's home and so you are very unlikely to catch Athlete's Foot in somebody's house, even if the owner has the condition.
What is more, people who are not wearing socks are likely to put on sandals when they leave, as opposed to closed shoes. Thus, they will not create the right environment for the condition to thrive.
Of course, if you are worried about it, you can always bring some slippers or socks when you visit a shoes-off home.
People who have a shoes-off policy ought to let their visitors know in advance and be willing to lend a pair of clean socks.