There is a simple rule which should be known by all, that is, to take your shoes off at the door. The host should not need to make this request explicit, but presume that all share the same etiquette. However, this is not custom in British culture; guests tend to leave their shoes on upon entering someones house, and so the awkwardness of asking the guests to remove their shoes arises.
I understand the reasons behind keeping shoes on; people feel exposed without them, they have verrucas, athlete’s foot or some other fungal disease they would rather not exhibit for all. Nevertheless, there should be an overriding factor of politeness to not tread dirt and bacteria from the outside all over someones house, for the sake of concealing their own insecurities. For instances where the guest does have infectious warts and whatnot, they should bring socks or ask for slippers; walking grubby shoes around the house is equally as damaging as spreading the infection.
There are of course always exceptions to the rule; pet owners are more likely to be accepting of shoe-wearing guests or if the host has shoes on, then you can probably assume it is acceptable for you to keep yours on. Besides this, guests should take the initiative to remove their shoes as soon as they enter. The home should be treated with respect and separate from the outside. I am quite certain that the majority do not wear shoes inside their own home, and if they do, I wonder whether it is included in their daily routine when getting dressed? I for one keep my shoes by the door and only tend to put them on when leaving the house.
I stumbled upon a blog which lists lots of reasons why the host may not want guests to keep their shoes on, in case you were wondering why I am particularly infuriated by this issue. I have been raised to practice the rule that shoes should be removed in the first instance, even before saying hello. The formality of shoes makes me uncomfortable and the thought of spreading dirt around for my son to play with sends my OCD into overdrive.