Instead of simply checking the number of search results, there are better ways to check how competitive a keyword is. Some keyword tools list a KEI (Keyword Effectiveness Index) score for competition level. Unfortunately that is merely the search volume divided by the number of search results. So it is just as ineffective as just looking at the number of results.
To get a quick gauge of how competitive a keyword is, you can try using Google search commands such as in anchor and in its title.
These commands will tell you how many webpages use that keyword in their title or in the link anchor text. Use them together in the same search to see how many sites are actively targeting that keyword through links and on-page optimization. Unfortunately this only tells you the number of active competitors. Among those active competitors, there may be a lot of websites with only several links or websites who have not optimized their entire page for that phrase.
For a more detailed competition analysis, you need to take a good look at the top ten websites. You should be checking how many links those websites have, both to their homepage and to the specific ranked page. Then check how strong those links are. Analyze the PageRank of their links, the relevancy of the link pages, the number of links per page and the usage of the keyword in their link anchor text. Also analyze those competitors for on-page factors such as their keyword use throughout the page.
Doing this kind of analysis manually can be quite time-consuming. To speed up the process you might want to install the SEO for Firefox browser add-on. This will display useful stats about each website within your search results. You may also want to use paid software such as SEO Elite to fully analyze a website's links. This will provide a very detailed breakdown of what kind of links they have and what keywords they are optimized for.
Conclusion
If there is a great importance of competitor analysis with regards to your marketing efforts, you need to ensure you are going about it correctly. The search engine optimization industry is full of misguided advice. Many people still tell you to check the number of search results, but this is a poor recommendation. Checking competition levels all comes down to determining just how strong the top ranked websites are. Although it sounds nice to say, you outrank millions of competitors, in reality you are only trying to outrank the top ten websites.