If you are checking how well your site is doing in the search engines as far as ranking so, you need to be aware of a couple of things that the search engines do:
1. They geotarget. This means that the search engine results will vary from town to town and from country to country. This is because the search engines, particularly Google like to make the search results more relevant to a region. If you are checking how you rank in the search results them you need to keep this in mind. Where you check from will affect what you see on the search results page.
2. They personalize. This means that what you see on the search results page is partly influenced by what you have searched for and clicked on previously. If you have searched for you own website and clicked on it before, especially many times, then Google will probably rank your site higher for you. Checking it from another computer may give a different result.