Many small businesses operate for years without registering a their business name, logo, or trade dress with the USPTO, and for many of those, the question of whether they have any enforceable rights regarding their business name, even though it has gone unregistered.
In short- yes, a trademark does not need to be registered to exist. A trademark exists once a business has used it in commerce to identify a product as having a provenance from a certain entity. If you have put your business name or logo on a product so that people know the product comes from you, then you probably have a trademark. Although there are other legal questions that a lawyer will need to consider to determine the validity of a trademark, the underlying concept is that a trademark can spring into existence regardless of whether it has been registered or not.
So why register? Although a trademark can spring into existence without registration, the enforceable rights of that trademark are limited. Without registration, a trademark is geographically limited to the areas where is has been actually used. Contrast that with USPTO registration, which grants exclusive rights to the mark anywhere in the US. Another major difference between a registered mark and an unregistered mark are the legal remedies available if someone infringes on your mark and tries to use it as their own. Legally it is much much easier to stop an infringer from continuing to infringe and to pursue monetary damages if a mark is registered. US registration can also be used to seize imports provide other protective injunctions.
Are you behind the eight ball if your mark is not registered? No. Do you have to register your mark? No. However, if your business is growing, it is often a very wise move to claim as many legal rights as possible by registering in the USPTO national registry. This prevents others from claiming the same mark and preventing your business growth and very importantly, ensures that you can claim certain exclusive online rights including how the mark comes up in search results.