Sometimes this information is harder to find. If your company is private or smaller, expect to have more trouble.
Public companies usually name their primary competitors in their SEC filings, usually the 10-K. But that list will be incomplete at best for various reasons. Private companies have no obligation to make this information easy to find, and most do not.
To get a broader picture of the competition, use directory databases to find out which other companies are in the same industry, and then look at them more closely to see if they are truly competitors ... they may not be competitors because of geography, because each company primarily sells to a different client-base, or for other reasons. (For example, Microsoft and a local computer retail/repair shop are nominally in the same business. However, neither would ever consider the other a competitor!)
By the way, you will often need to know the SIC or NAICS code for your company (click here for more information about SIC and NAICS). Then you'll be able to find out which companies are in the same industry.
Both of the databases below have quick lists of competitors. The competitors listed will be the major ones, but the lists will not be comprehensive, nor will they necessarily cover all industries in which your company has a presence.