Live filtering of nodes by taxonomy terms?
What you're after is known as Faceted Search. You're able to drill down your Views results based on taxonomy terms (or other fields for that matter) as you described.

A good example of Faceted Search can be found within the Commerce Kickstart demo store.

You'll need the Search API module as a basis, and I found a really good tutorial on getting started with Faceted search here: http://vimeo.com/15556855

If you're setting up a site which will get a lot of traffic, you might want to consider using Apache Solr to take some stress off your database when performing search queries.