All bloggers follow a golden rule More Keywords, More Traffic. This makes them to expand their content in new niches and get ranked on variety of keywords for more traffic. Choosing right Keywords and placing them on a page with adequate balance increases its visibility in search results. But even if working hard on it doesn't help for you, then?
Search engines first find every related page to search query. Then the results listing order is determined based on the query and matching words within various pages. So, it is a good idea to check for those words which are boosting the rival's page rank. You then can use similar keywords.
StatMyWeb is an online tool that gives out such type of information for any website or blog. Here, you can see not only keywords ranking of the site, but also daily revenue of the site, PageRank, Alexa traffic details, Meta tags analysis, indexed pages (by Google, Yahoo and Bing only), W3C validation, and many other details about the domain.
Let me know about other similar tools you are aware of.