Is there a free way to determine how your site is ranked by search engines?

Yes you can track ranking for free but this one is a a free software with option to go for other premium edition. In free version you can track up to 5 domain. There are other helpful feature related to seo as well.

Maybe you just go to the following url and go to bottom and read the "Quick Start Guide" at the bottom first. Go to step 7 for checking ranking. If you think that is what you need you can download then.

http://www.webceo.com/download/index.htm

Anyhow be careful when using software using some kind of automatic checking to any search engine. Search engine don't like auto robot calling them often cause it will eat their resources and slowing down their services. When that happened they usually will blocked that IP for maybe 1 to 2 days. You will notice this when you can't access them for example when trying to use google search. So please don't go crazy checking your ranking.

The Google page rank is a rough measure of a ranking, each page of a site is ranked separately. (Google is actually recommending one not rely too heavily on their page ranks)

Alexa also ranks site with a more precise number system that allows you to see day to day variations (though I don't actually how often their stats are updated)

Enter in your search engine: Page Rank Lookup to find online tools that might do the job

Professionals use free plugins for the firefox browser to get these rankings, you can visit alexa.com and look up a site.

Small sites will have no ranking at all in these systems, but may still appear in a back page of the search results.

Yahoo site explorer is handy for getting a count of incoming links to your site, a valuable indicator of it's potential rank.

The Search engine algorithm is a very complex system that is constantly changing. Only search engines knows the exact details of their algorithm. SEO’s only has various facts which are the result of several experiments, experience, and few tips from search engines itself. In general, search engine rank websites based on popularity and relevance together with trust. If you want to know more, have a look at our website now.

Well you can install the Google toolbar to determine your page rank or your competition's PR. I would suggest using Google analytics to determine search results. Do searches in Google such as search:www.yoursite.com or link:www.yoursite.com. Find out your websites value and see who links to your site. You have to remember that you need to focus on Yahoo! and MSN as well in addition to Google, since about only 80% of people use Google. Your efforts certainly should be focused on Google SERPs but don't leave the others out.