Way too many to list. The usual suspects include: Amazon, Westjet Airlines, Southwest Airlines, Apple etc.
I'm focused on new(ish) tech companies and their approach to customer service such as: Silvercar, Airbnb, ZenPayroll, Oscar.
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.
The companies that rank best for customer service put the customer at the center of their mission and operations. Zappos does this incredibly well. Their mission is "to provide the best customer service possible," and they've made sure that every decision within the company maps back to that mission. They empower reps to use their best judgement and don't use scripts. While Zappos isn't ranked by the American Consumer Satisfaction Index, its parent company, Amazon, is and scores highest among all internet retailers. (http://www.theacsi.org/index.php?option=com_content&view=article&id=149&catid=&Itemid=214&c=Amazon)
I wrote a blog post recently that compares Zappos with the worst performer on the index, Comcast. You might find that useful for further reading. http://yourbrandvox.com/blog/2014/7/16/zappos-vs-comcast
Here are 12 of the top companies with killer customer service techniques: http://www.fieldboom.com/blog/customer-service-examples/. The list includes Amazon, which shouldn't come as much of a surprise.
Features consumers now take for granted – such as product suggestions, customer reviews, and one-click checkout options – all have their origins in Amazon. Going back to our definition of customer service, consumers had no idea such convenience was even possible before Amazon implemented these services and made them par for the course.
While Amazon has its fair share of feel-good customer service stories, it’s the innovative, forward-thinking, customer-facing approach CEO Jeff Bezos and company take that earns them the top spot when it comes to customer service.