It depends on the area you live in; and that house's circumstances. For instance, in Canada; most people take off their shoes (Because we live in a cold environment, we have carpeted floors (In most rooms)and like to keep them clean) - but in the US most people leave their shoes on (Because the majority of people living in America don't have carpeted floors - they usually have wood or tile).
It also depends on the person, the current scenario - and/or the religious customs of the people living in the home (In some religions it's highly offensive to even walk into the house still wearing shoe's (You would have to take them off and carry them inside)).
But overall there is no normal thing to do with your shoes. If your more comfortable with your shoes off in a home, than take them off. Otherwise, keep 'em on.
But anyways - if you are going into someone's house, it's polite to take your shoe's off unless they say it's okay (Even if they do say it's okay; if your shoe's are moderately or more dirty - take them off).
It also depends on the person, the current scenario - and/or the religious customs of the people living in the home (In some religions it's highly offensive to even walk into the house still wearing shoe's (You would have to take them off and carry them inside)).
But overall there is no normal thing to do with your shoes. If your more comfortable with your shoes off in a home, than take them off. Otherwise, keep 'em on.
But anyways - if you are going into someone's house, it's polite to take your shoe's off unless they say it's okay (Even if they do say it's okay; if your shoe's are moderately or more dirty - take them off).