Many people, mostly Americans, believe that every family was once issued a coat of arms and then everyone born with that family name automatically gets to use the same coat of arms. If you believe that, it is time to correct the myth.
NOTE: There is an exception. I am told that Samurai families in Japan do have family coats of arms although they do not resemble British or European coats of arms. In any case, if your ancestry is 100% Japanese Samurai, the rest of this article does not apply to you.
To begin with, coats of arms are never issued to families; they are issued to individuals. Coats of arms are issued by heralds and there are different heralds in each country in the United Kingdom and in Europe. A coat of arms is granted by the King of Arms in England and in Ireland, while the court of the Lord Lyon King of Arms grants that right in Scotland.
England, Northern Ireland, Wales, and Scotland have the most rigid system of heraldry (coats of arms). Other European countries do record and permit coats of arms, but do not restrict their use as much as do the English and the Scottish heralds. A repository called the College of Arms holds an official register of all granted coats of arms that exist in England and Wales.
The United States has never accepted the concept of nobility and therefore has no officially-recognized heralds. Several American organizations claim to be able to issue coats of arms but any such arms issued by an American organization have to be considered as "unofficial." There is no official issuing body in the U.S. Most Americans who wish to obtain legitimate coats of arms apply first in the name of a foreign-born ancestor with the heralds in the country where that ancestor lived. The American descendant may then apply to use the ancestor's coat of arms as his own as his "inherited right to arms."
Throughout history, an individual could apply for a coat of arms and the heralds would decide whether or not to approve it. Coats of arms generally are issued to men although there are numerous exceptions. The Queen of England always has a coat of arms, as do many high-ranking officials. For instance, Margaret Thatcher was issued a coat of arms when she was prime minister.
In medieval days, coats of arms were issued only to knights and to noblemen as an emblem to be displayed on shields and on various banners for use in battle. After all, it was difficult to see through the eye slits in the helmets they wore and every soldier wanted to make sure he was swinging the broadsword at the enemy, not at his commanding officer. The brightly painted coats of arms helped identify the combatants back in the days before uniforms.
As the years passed and the battles decreased, a wealthy merchant class began to flourish and many merchants obtained coats of arms as well. So did clergymen, elected officials, and a few others. In every case, the coat of arms has always been issued to an individual, not to a family. You might find a coat of arms issued to someone with the same family name as yours, but that doesn't mean that you are entitled to use the same arms.
When a man is entitled to display arms, his sons also may apply for coats of arms. Note that granting of coats of arms is not automatic, each person must apply. Sons usually are granted coats of arms that are very similar to their father's but are changed slightly, to add some small detail that shows that this is the shield of their own branch of this particular family. If a man has multiple sons, each son applies for his own coat of arms with slight differences, even different from those of his brothers. The use of slightly modified coat of arms is called "differenced arms."
When the father dies, the eldest son may then apply to use exactly the same coat of arms that his father used. Once granted, he stops using his differenced arms. His younger brothers continue to use their differenced arms, however.
Obtaining permission to use your deceased father's coat of arms is not automatic. For instance, each King of England traditionally uses his own design and does not use that of his father.
There have always been a few instances in which women could inherit a coat of arms and to use them. However, a woman can not pass them along to her children unless she has no brothers. If this is the case, the woman owns the coat of arms, to pass along to her children, and she is considered to be the heraldic heiress to the coat of arms.
The wearing or display of coat of arms is restricted in most countries that recognize the ownership of coats of arms. There are no such restrictions in the United States; you may wear someone else's coat of arms, if you wish to. Even the countries that do restrict usage rarely enforce such laws. Therefore, the sale of bogus "family coats of arms" is rarely stopped by the authorities.
In the countries that do restrict usage, only one person may use any particular coat of arms although a grantee's sons or younger brothers might be using similar, but differenced, coats of arms, assuming they have applied for and received permission to use those differenced arms.
Did you ever receive an ad for "your family's coat of arms?" That ad isn't worth the paper it is printed on or the electrons used to display it on your computer screen. Regardless of your last name, you should display a particular coat of arms only if (1.) you have applied to the heralds for permission to display the particular arms and (2.) if such permission has been granted. Once that happens, you are the only person in the world authorized to display that coat of arms.
Displaying arms without proper authorization is a form of impersonation; you are trying to identify yourself as someone else. Legal or not, such impersonation is always in bad taste.
For authoritative information about heraldry (the display of coats of arms), I suggest you look at the following:
Polish Genealogy and Heraldry Society: http://www.feefhs.org/pol/frg-pghs.html
Luxembourg Society of Genealogy and Heraldry: http://ourworld.compuserve.com/homepages/hotel_claravallis/genealog.htm#genealogy
Institute of Heraldic and Genealogical Studies - Encompasses all aspects of genealogical and heraldic research, art and practice: http://www.ihgs.ac.uk
Heraldry Society of Scotland: http://www.heraldry-scotland.co.uk
Heraldry Australia, Inc. - Australian Heraldry Society: http://www.heraldryaustralia.org
Heraldiska Samfundet - Swedish academy for the science of heraldry and related subjects: http://www.heraldik.se
Slovenian Society for Heraldry, Genealogy and Vexilology: http://genealogy.ijp.si/hslov/all/index.htm
The Birmingham and Midland Society for Genealogy and Heraldry: http://www.bmsgh.org/
Scandanavian Heraldry Society: http://www.heraldik.org/
Office of the Chief Herald of Ireland: http://www.nli.ie/en/heraldry-introduction.aspx
The Augustan Society - An international genealogical, historical heraldic and chivalric society: http://www.augustansociety.org/
South African Heraldry: http://www.geocities.com/heraldrysa/
Heraldry Society of Sweden: http://www.geocities.com/Athens/Forum/1284
Cambridge University Heraldic and Genealogical Society: http://www.cam.ac.uk/societies/cuhags/
Russian College of Heraldry: http://www.armorial.ru
Slovak Genealogical-Heraldic Society: http://www.genealogy-heraldry.sk/
Heraldry in South Africa: http://freepages.family.rootsweb.ancestry.com/~heraldry/page_optima.html
South Australian Genealogy & Heraldry Society Inc.: http://www.saghs.org.au
Royal Heraldry Society of Canada: http://www.heraldry.ca
The American College of Heraldry - a non-profit body with the aim of aiding in the study and perpetuation of heraldry in the United States and abroad: http://www.americancollegeofheraldry.org
Croatian Genealogical and Heraldic Society - CGHS: http://feefhs.org/cro/frg-cghs.html
CUHAGS - The Cambridge University Heraldry and Genealogy Society: http://www.cam.ac.uk/societies/cuhags/
The Heraldry Society - The Heraldry Society exists to increase and extend interest in and knowledge of heraldry, genealogy, ceremonial and allied subjects: http://www.theheraldrysociety.com
The College of Arms - England. Holds the official register of all Coats of Arms or heraldry in England and Wales. Also grants arms to individuals and organizations: http://www.college-of-arms.gov.uk