It depends solely on the keyword and the focus on that keyword that the site has given.

Try searching "AdventureQuest" on any search engine, and www.battleon.com will surely be the #1 result. This is because AdventureQuest is the primary keyword (being the title of the site) and is the primary focus on by the webmaster.

So, to answer your question, Yes, it is possible for a site to be the #1 in searches.

However, if you meant Technorati Rank or Alexa Rank, then it depends on the factors considered by the Ranking system. To know more about those, you'll have to research on the different systems. I can tell you now though that it will be very hard to achieve #1 in various/all ranking systems.