Well this industry is pretty big and there are number of companies that are known for their customer support. Remember, there are two aspects to customer support one is Preventive and the other one is Reactive .
Most of the time you may not come to know explicitly about some of the Companies doing very well on Preventive measurements. This in fact, reduce the occurence of problem to a great extent, and even the clients at times don't realise that their company is running a very tight ship.
In terms of Reactive, there would be one where most of the support would be client specific, like requiring some scripts to be installed and other client specific troubles. Other would be, in area where there is issue or problem affecting multiple customers. In both the cases, the comapany needs to be blazing fast in responding any of clients queries. The key aspect for company is a) to understand clearly what client needs and then b) provide optimal solution suiting clients specific requirements.
I would suggest to keep above in mind while looking company with top notch customer support. I would suggest you to spend some time searching this forum about some of customer support stories, reviews on their services, their uptime and so on.
Then prepare a short list of your prospective hosts and have discussion at WHT about them.
When I first started out, I used Eleven2 which has extremely fast support. They also offer quick support via AIM if you need that. Highly recommended!
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Usually the customer contact their host providers when something goes wrong or when they have a question, this is the prime responsibility of the company to understand clearly the specific needs of the client and to provide optimal solution to their satisfaction level.
You can also enhance your support by adding a complimentary support with the regular support that can differentiate you from (others).