I don't have any quantifiable data on this matter, so please do take this with somewhat a pinch of salt.

Buffer is well known for it's customer service. They often release reports of their response times and customer satisfaction rates to the public.

Here's a post from one of its co-founders: http://blog.bufferapp.com/customer-support-on-twitter

Response time is one thing, but of course, that doesn't cover the quality of support.
I've found "Pocket" do have great quality of customer support and when I first started using Optimizely I was blown away about how willing they were to help their customers.

These are just some of the brands that come to my own mind based on a combination of my personal experience and general market observations.