My host has 24/7 support using live chat, emails, a ticket system, and phone #. It works well and they are always available to help. Customer support is definitely something that I consider when looking for a host, and live chat is a big plus. I normally use that first before going on to another method of communication.
Customer satisfaction is the greatest thing in hosting industry. Replying to client queries and concerns within time is very important to keep up the good reputation and get more registrations.
I'm with NameCheap, and while I don't need the support all that much, when I do need it, it's professional and fast. I love their live chat, so that I can get to the tech directly without having to send emails back and forth for long time.
I'm running my servers off Ramnode (VPS, not web hosting, although I run a webserver off of them as well). The customer service is pretty good; I think the longest I've waited for a response to a ticket is 2 hours.
I use Ipage hosting, they have all of questions and answers for supporting. But if something out of those list, you need to call them. That's good way to help customer, but other side it's uncomfortable because I'm not in USA. If they provide an email, it will be perfect.