One of the biggest myths in the SCA is that you must register a "device". A device is the SCA term for armory, be it a coat of arms or a simple badge. First and foremost, the answer is you may register armory if you want to. To many in the College of Arms and in the SCA, this is heresy! But lets look at things a little more realistically. In a historical context, not everyone had heraldry. Suppose your persona is to be a 7th century Spanish vintner. It is highly unlikely that such a person would actually have arms. They might have an identifying mark for their wares, but a formal coat of arms would be unusual, not to mention impossible given that formalized heraldry did not exist until the 1200's!
Within the context of the SCA, armory is very useful. A badge is used to identify members of a household or to mark personal property. A coat of arms is used on a banner, gonfannon, shield, or tabard to identify a person or group. If you are a fighter, using armory is almost a necessity so your companions(and opponents) on the field can identify you. It is very difficult to recognize a face inside a helmet from ten feet away, and with some helms even five feet away is a problem!
There is a great deal of pressure on the newcomer to create heraldry--many kingdoms will only provide promissory scrolls for awards if a person's heraldry(and/or name) is not registered with the SCA College of Arms. My response is: "So what?" When I received my Award of Arms, neither my name nor my device were registered. One result of this pressure is a "quick fix" in which people end up with inauthentic looking or "clever" heraldry whose novelty wears off quickly, or worse yet, heraldry they don't really like.
The longer a person stays in the SCA, the more dissatisfied with inauthentic arms they become. It is just a natural progression of "familiarity breeds contempt." Sort of like a chip in the paint on a wall will eventually become irritating. The key to preventing this phenomenon is to do some research. Find out what sort of armory your persona would be likely to have. If your persona would not have had arms, try designing a badge rather than a formal coat of arms. Choose elements you like and that are consistent with the time and geographic region your persona lives in. A 13th or 14th century Scots nobleman would in all likelyhood have a lion on his coat of arms, whereas a German nobleman from the same period would probably use an eagle.
You do not have to conform to temporal and geographical heraldry. There is still room for "fantasy" armory. However (and I bet you saw this coming) if you want to register your armory, you will need to follow the rules as set out by the SCA College of Arms. The primary goal of the CoA is to ensure that each person has a unique name and armory within the SCA. In order to acheive this goal, the CoA performs conflict-checking to prevent people from using armory that is too similar to other individuals's arms.
Some of the underlying principles of the College of Arms are as follows: historical validity(style), documentation, non-offensiveness, and uniqueness. These principles are the basis for acceptances and returns of submissions within the SCA.
Master Arval d'Espas Nord eloquently explains in this exceprt from The Compleat Anachronist, #22, Heraldry:
The individual elements and the overall design of each device or badge must have been used in medieval heraldry, or must be shown to be consistent with medieval heraldic style. Charges should not represent modern objects and should not be drawn in a modern style. Only standard heraldic tinctures and field divisions may be used. Heraldry submitted must not violate medieval design standards of balance, complexity, or contrast.
The members of the College of Arms will often assist the submitter in this task by providing extra documentation with their comments, but the submitter should not count on such help.
If you are not entirely sure that your submission follows standard medieval practice, you may be asked to provide extra documentation to justify your design. "Standard practice" is a term that gets bandied about a good bit. For an idea, take a look at examples in some of the standard (and easily available) heraldry texts.
The College does not regulate taste; this principle prevents the registration of truly offensive heraldry. This restriction includes designs that are excessively religious, obscene, or morbid; that have strong political or social connotations; and that appear to claim honors the bearer has not earned in the Society.
No device or badge should be so similar to any registered Society emblem as to cause confusion between the bearers, nor so similar to any historical or fictional emblem as to imply identity or close relation of the bearers. The definition of "too similar" is explained in the Rules for Submission, and, given the evolving nature of those rules, is not always clear-cut.