KeywordSpy is good - it lots you do comparisons between your site and your competitors too!
You need a software program like Web Position Gold or Market Samurai. Also install google analytics to your site to see what keywords your traffic are finding you under. There isn't software or a site that I know of that will automatically find what keywords you are ranking under without you programming it in software.
*I'm looking for a tool that will tell you every keyword your website ranks for.*
To answer the original question, there were several updates to the free Google's Webmaster Tools. You have to put a verification code on your website to verify you're an owner and then these Webmaster Tools allow you to see your top keywords, positions, clicks, clickthru-rate, etc. All data is obviously only from google.com.
You can also install Google Analytics (also free) to see more keyword-related data on other search engines.
Have you also looked at Wordstream's Keyword Niche Finder?
Just to be authorize though, I don't think there is a plan that will tell you what you rank for.... you have to invest in the keywords that you are trying to rank for and it will order you if you are ranking and in what lays. I use IBP and Market Samurai. some are splendid.