A crest is part of a coat of arms. The words "family crest" are a misnomer. Also coats of arms usually do not belong to families and definitely they don't belong to surnames. So beware of peddlers selling coats of arms(they use the misnomer family crest) on the internet, at shopping malls, in airports, in magazines etc like they belong to everyone with the same surname. They don't.
In British countries a coat of arms is granted to a specific individual not to a family and are inherited by individuals. In continental countries they are frequently assumed by individuals.
The term "family crest" probably came into existence when a man was granted, assumed or inherited a coat of arms, he frequently had the crest portion put on his family's silver, napkins etc. But by and large the coat of arms belonged to him, not to his family.
Frequently more than one man with the same surname, not all necessarily related, were each granted or assumed their own coat of arms, all different. No one peddler who sells them will have all of them. They don't need to in order to sell to suckers. The only time they will have more than one associated with the same surname is if more than one man with the same surname from different national origins were granted or assumed a coat of arms. Then they will have one of each and there might have been 50 others. Most men with that same surname are not entitled to a coat of arms at all as they have no direct male line ancestor that was ever granted or assumed a coat of arms.
There has been an ad running on TV, saw it in the wee hours of the morning recently, for a company selling framed surname histories which is rather shady as not everyone with the same surname shares the same family history. When surnames were taken or assigned in Europe during the last millennium, it wasn't impossible for legitimate sons of the same man to wind up with a different surname and still each could have shared his surname with others with no known relationship. So the root person of your surname will not necessarily be the root person of someone else with your surname. The man in the ad states "a" coat of arms will be on it not "your" coat of arms. You see on TV the FCC can slap a company hard for fraudulent advertising. The FCC has no control over the internet or some merchant in your local shopping mall.
Here are some links to various countries heraldry.
http://www.college-of-arms.gov.uk/Faq.htm
http://www.college-of-arms.gov.uk/About/12.htm#a
The College of Arms grants coat of arms for England and Wales.
http://www.lyon-court.com/lordlyon/216.181.html
The Lord Lyon grants coats of arms for Scotland. If your name is Scottish and you ever visit Scotland, you better keep any tattoo covered up. They can file criminal charges against you for displaying a coat of arms just because you found one with your surname over or under it. They do have clan badges in Scotland.
http://www.nli.ie/en/heraldry-introduction.aspx
http://www.heraldry.ws/info/article10.html
The above links are regarding Irish heraldry. In Ireland there are arms that had been granted to individuals but they also have clan arms.
http://www.regalis.com/onom.htm
This is regarding Italian heraldry.
The only way to know if you are entitled to a coat of arms is to trace your ancestry back to the person who was originally granted or assumed one. Different countries have different rules but to display a coat of arms without documented proof that you are entitled to it is considered usurpation of another's identity. Certainly if you have pride in yourself you don't want to take on another's identity.