Talmud

Thus said R. Yohanan: One gives precedence (i.e., honor of the first entry) only in a doorway in which there is a mezuzah (or which is eligible for a mezuzah).

Women are exempt from reciting the Shema and putting on tefillin,1 but they are subject to the obligation of prayer, mezuzah, and grace after meals.

He who is observant of [the precept of] mezuzah will merit a beautiful dwelling.

Our Rabbis taught: “Who is an am haaretz (ignoramus)? R. Nathan said: Whoever has no mezuzah on his door.”

R. Chiyya maintained: “It [the death of young children, G‑d forbid] is for the sin of [neglecting] mezuzah2... as it is written ‘so that... the days of your children may be multiplied...’ (Deuteronomy XI, 21)”

Seven are banned by Heaven: [one of them is] a Jew... who has no mezuzah on the door...

Every single Jew is surrounded by seven mitzvoth. He has tefillin on his arm and head, a mezuzah on his door, and four tzitzith on his garment. Therefore, King David said (Psalm 119:164), “I will praise You each day with seven.”

Some put a mezuzah on the doorpost, and “sin crouches at the door.”

G-d says: If you come to My House I will come to yours. (Hillel the Elder)

Tefillin and tzitzith are limited in time [as they really can be done only at certain times – during the day, for example], but mezuzah is not [as it always can be done]

“Our Rabbis taught: If a landlord rents a house to his neighbor, the tenant must provide the mezuzoth. But when one vacates it, one must not take them with him, except when he rents from a Gentile, in which case he should remove them.”