Whether you're a multinational Internet retailer or a lone human just entering the Web world, there are many things to consider when purchasing a new domain name, not the least of which are core SEO (search engine optimization) parameters. Following is a list of considerations I'd supply to either entity mentioned above or anyone in between. Some may seem ridiculously obvious, but a friendly reminder won't hurt.

• Keyword research: Does the domain use popular and focused keywords? Make sure the domain and its associated URLs will be conducive to search engine visibility. Check it on tools like Overture Keyword Selector, Google Suggest, WordTracker, and Keyword Discovery.
• Linkability: Does the domain have appeal to bloggers and Webmasters who might consider linking to you? Links are crucial to your site's SEO. For example, NeopetsFanatic.com has link appeal, whereas free-neopets-cheats-hints-tips.info does not.
• Top-level domain: Choose the proper top-level domain (.com, .net, .org, .info, and so on). If your business is in the United States, then you should use .com as your domain. While there is nothing wrong with .net and .org domains, they are not perceived as being as "professional" as .com domains. The .org domain is still perceived as nonprofit. Sometimes that is a positive though--such as for my blog ChangesForGood.org, because in that case I wanted to distance the blog from any commercial interests. Top-level domains like .info and .biz are often associated, rightly or wrongly, with spammers.
• Used URLs: Check indexation levels of a domain name to see if anything is still indexed. Use query operators to check your site even if you're not buying it from a secondary source (DomainName.com). Or simply use an indexation checker like URL Check.
• Site age (if a used URL): Run the URL through The Wayback Machine. Make sure there aren't any previous associations with pornography, hate or violence. If there are, avoid the domain.
• Back links (if a used URL): Make sure a previously used URL doesn't have negative (see above) links coming into it. Use the query operators DomainName.com to check this.
• Blacklists check: See if the URL or its associated IP address has been blacklisted at a site like Moensted.dk .
• Relevancy: Make sure your domain name is relevant to your business. Don't buy a URL because it sounds cool or it has personal merit. Buy it because it has direct, focused keyword relevance to you business.
• URL length: On the other end of relevancy is the issue of being too specific. Don't get too long and detailed at the top; you can always get more specific as you go deeper into subdomains. Shorter domain names are also easier to remember--and type!
• Potential for legal conflict: Be aware of trademarks and copyrights belonging to other entities. While a URL like www.amazonbooks.com might be accurate to your bookstore in Amazon, Canada, it's also an issue with an existing business. Use the search engines to research the keywords contained in your URL. If something comes up that seems like a conflict, it most likely is.
• Double meanings: Does your keyword-rich URL have a secondary meaning? For instance, let's say you're starting a Web site that helps people to locate psychologists in their area. You come up with www.therapistfinder.com. But look more closely. Is there a second meaning in the URL? When joining words without a hyphen, take a step back and look again.