A DigitalPoint Forums thread asks a great question, "what if the competitor is Google itself?" Yea, what if you have a product or service you are selling, but you have to go against Google in the search results at their own engine?
The specific example given in the thread is for a search query at Google.com for mobile videos. For me, the first and second indented result is from YouTube. The third result, is an adult site. I am not sure, but that can possibly be his site. Before hand, he ranked in the number one slot and his traffic dived when Google's YouTube overtook that first and second position.
Let's take other examples:
Google bought Urchin and made Google Analytics, a search on analytics brings up Google in the number one slot. But a search on web stats brings up Google in the 7th position. Fair, I think that is fine. What about a search on news, which returns Google News in the second position. Isn't Yahoo! News way more popular? How about maps which returns Google as number one and MapQuest as number two?
There are tons of examples, but the super example is search engine where Google ranks number five for me and MSN ranks number one.
FYI - make sure your personalized results are not changing what I report above, also geo specific data may change the ranking information above. Finally, this is a dated post, so rankings change over time.
What can you do to out rank Google for products you sell that they also sell? It can be done, but it will be hard.
Forum discussion at DigitalPoint Forums.