When should I be using the Transients API?

I’ve never used the Transients API before and was wondering if anyone has guidance on when to use it. The Codex article implies that as a theme developer I might want to set each new WP_Query() as a transient; I assume the same might be said for direct $wpdb queries and query_posts(). Is that overkill? And/Or are there other places I should default to using it?