According to United States Code, a trademark is "...any word, name, symbol or device used in trade to indicate the source or origin of goods or services, and to distinguish them from the goods and services of others." Examples of current or past trademarks include:
Words
Symbols/Logos
Slogans
Names
Colors
Unlike patents, trademarks are not limited in duration. They are valid as long as the trademark continues to be used in commerce and maintenance fees are paid regularly. Similar to patents, trademarks are also administered by the United States Patent and Trademark Office (USPTO). Information about United States trademarks is found on trademarks section of the USPTO website.
A registered U.S. trademark only provides exclusive legal protection in the United States. One can search for foreign registered trademarks in the World Intellectual Property Office's (WIPO) Global Brand Database.
If you intend to seek legal protection for your trademark outside of the United States, you must apply for this with foreign national intellectual property offices. This can be achieved via the Madrid Protocol of which the United States is a signatory country. It allows for the international registration of a trademark through the USPTO's Trademark Electronic Application System International (TEASi) in English rather than in the official language of each intended country.
It's important to remember that not all applications are accepted by the USPTO as trademarks especially if they are merely descriptive of the product or if there is a likelihood of confusion by the general public with another existing unrelated trademark. Also, even if a trademark used in commerce is not registered with the USPTO it is considered common law usage which provides legal protection in the local geographic location where it is used.
All information pertaining to researching U.S. trademarks is contained on the USPTO's Searching Trademarks page. The Trademark Electronic Search System (TESS) is used to search for registered trademarks or pending trademark applications.
If you have satisfactorily conducted a search for a word or logo trademark and you have found nothing similar in the TESS database, your search is not yet over. You have simply determined that there is no registered U.S. trademark matching yours. You also need to search other resources such as the internet to determine if another similar trademark is being used in commerce. As mentioned on the introductory page there exist common law trademarks, while not registered with the USPTO, which still carry some legal precedent for the owner who can prove through documentation that they have been using the trademark longer.