An interesting thread over at WebmasterWorld named How Many Matches Indicate High Competition?, discusses how someone defines the competitiveness of a keyword phrase.
John_Caius provides three classifications to determine the level of competition for a keyword phrase.
My general rule-of-thumb definition of low competition would be where the top ten returning results haven't been SEOed. Medium competition would be where the top ten returning results have been SEOed. High competition would be where the top hundred results have been SEOed. Really high competition would be where a major site, like Amazon, Yahoo or WW is targeting that keyphrase. That's a better guide than number of results, because it tells you about how hard everyone else is also trying to be number one.
Finding the keyword phrase that is not SEOed but is a big bread-winner is where it is at, but I will leave that to Dan Thies to talk about. I had a law client that was paying a fortune for a few targeted keywords with AdWords. They were very competitive PPC campaigns but to my surprise, no one was optimizing for those keywords organically. So we quickly changed some title tags around and presto, free traffic. Soon enough the competition caught on, but it was fun to see. Many SEMs/SEOs have stories like this to tell.