United States Postal Service regulation upheld by the Supreme Court in 1981.
Section 508.3.1.3 of the Postal Service's Domestic Mail Manual
3.1.3 Use for Mail
Except under 3.2.11, Newspaper Receptacle, the receptacles described in 3.1.1 may be used only for matter bearing postage. Other than as permitted by 3.2.10, Delivery of Unstamped Newspapers, or 3.2.11,
no part of a mail receptacle may be used to deliver any matter not bearing postage, including items or matter placed upon, supported by, attached to, hung from, or inserted into a mail receptacle. Any mailable matter not bearing postage and found as described above is subject to the same postage as would be paid if it were carried by mail.
Anyone caught delivering flyers, brochures or other materials to a mailbox can face prosecution and fines.
Here's what the U.S. Code says about the infraction:
"Whoever knowingly and willfully deposits any mailable matter such as statements of accounts, circulars, sale bills, or other like matter, on which no postage has been paid, in any letter box established, approved, or accepted by the Postal Service for the receipt or delivery of mail matter on any mail route with intent to avoid payment of lawful postage thereon, shall for each such offense be fined under this title."
Violations of the mailbox restriction law can be punished by a fine but not by imprisonment. The maximum fine for each offense is $5,000 for individuals and $10,000 for organizations.