I have been testing two auto tagging plugins recently.
The first if the WP-Auto-Tagger. This plugin uses the Yahoo! API to query content for common tags. It has a manual suggest button and an auto-tag feature that will automatically tag posts when they are published.
The second is the Calais Auto Tagger. Again this uses an API to operate semanic analysis on the post content and then suggests tags on that basis. One click to suggest tags, another to add them.
Mostly, I have been using the WP-Auto-Tagger and have been happy with the results. Although, using full auto-tagging may lead to some irrelevant tags. Generally, I use the manual suggest and then weed out the few that appear to be completely irrelevant.
I seem to get better results from posts over about 300 words as it gives the analysis engine more substance to work with.