The Talmud says that a mezuza attached in a way that looks like a "nagar" is invalid. Rashi defines "nagar" as a sideways bolt. According to this, a mezuza placed sideways would be invalid. Rather, one should place it straight up and down, so that someone walking in could read it.
Rabbenu Tam disagrees. He defines "Nagar" as a vertical bolt. He writes that placing a mezuza upright would be disrespectful, comparable to burying a person in a standing position. Rather, the mezuza should be placed like the Tablets were placed in the Holy Ark horizontally.
The Shulchan Aruch rules according to the opinion of Rashi - that the mezuza should be placed vertically. This is the accepted Sefardic practice and this is also the ruling of the Vilna Gaon. The Rama, however, cites the opinion of Rabbenu Tam, that a vertical mezuza is invalid. Taking this opinion into consideration, he states that the best way is to put the mezuza on a slant, with the word "Shema" towards the inside. Since the mezuza is neither vertical nor horizontal, it is valid according to both opinions.
I once heard a beautiful explanation of the symbolism of the slanting mezuza: The mezuza is placed on the door of the house - the house being the abode of husband and wife. The slanting mezuza "teaches" every couple how to create "Shalom Bayit" - tranquillity in the home. Each one should be prepared to compromise and "bend towards the other" in helping to lead a harmonious family life.
