A shameless plug here but hopefully to help the discussion going. @gosquared would be our favourite. Why? Well obviously because we made it. Users tend to like us because the platform is quite simple, intuitive and cost effective. We also provide rich data about a visitor's browsing behaviour.
I actually recall us talking about in a Median integration with Derek _years_ ago. Glad to see Median is doing so well.
My favorite chat tool is from Chat Metrics (chatmetrics.com), as they offer a 24/7 managed live chat service through their software. The service provides instant assistance to my website visitors, which makes it easier for me to convert them into customers by influencing their actions.
-It comes with 6 chat types I can interchange anytime
-Can be embedded on my website and events
-Has moderation tools where I can screen messages before it goes live, mute users, ban IPs, slow down chat, and more
-The support is excellent