You can have as many domain names as you like. You can have each domain name point to a different site, or you can have multiple domain names point to the same web site (but not to different pages within the same web site). Many companies register several domain names and have them all point to the same central web site. This is known as a "domain alias."
Registering multiple domain names for the same site not only brings the largest draw to your site, but it also can prevent competitors from poaching your potential customers. When picking multiple domain names -- or aliases -- for the same site, consider variations of your name such as common misspellings, as well as both singular and plural versions of the name.