At Less Annoying Software, customer service is very important to us for two reasons. The first is because we're pretty small and customer service is one of the ways we can set ourselves apart from our competition. The other reason is because the software we build is designed to make it really easy to organize your customer interactions, so we'd better be able to do a good job with that ourselves.
So because customer service is so important, we try to do the best job we can. We respond to emails and phone calls in a matter of minutes when possible. If someone finds a bug, it gets fixed immediately. If someone has a reasonable feature request, we generally have very fast turn-around time (sometimes same-day). Pretty much everyone that has ever contact us about a question or a problem has come away very happy. This is a great way to make sure our customers like doing business with us.
As a customer service person, I feel like I'm successful every time I interact with a customer. But as a product person, I feel like I've failed. Customers don't call us because they're interested in how my day is going. They don't call so that we can be pen pals. They're just as busy as I am, and they only call or email us because either they don't understand how our software works, or something went wrong. If we really had perfect customer service, that would mean we would never talk to our customers. Ever.
Don't get me wrong, I really enjoy dealing with customers (it's more fun that talking to my computer all day). But if someone calls me with a question, that means that we already messed up. It means we need to write better instructions, post better videos, or just rethink the software so that it makes more sense to begin with. If a company is really committed to offering great customer service, the main thing they should do is try to reduce the number of problems customers run into, not hire more people to help smooth over the problems after they occur.
Most banks have commercials about how they have helpful customer service reps on call 24 hours a day. That's great and all, but shouldn't they be addressing the root causes of the customers' issues (confusing fees, horrible websites, etc)? On the other hand, you almost never hear about Google's horrible customer service. When a product works, it's not a big deal that they don't have a support number for you to call. (Note: I realize there are some problems with Google products and they could do a better job of handling them, but you get my point).
Obviously, improvements to the product don't have to come at the expense of traditional customer service. You don't have to choose between acting like banks (lots of people answering the phones but horrible products) and Google (great products, no support people anywhere to be found). You can shoot for both, but it's just important to keep in mind that customer service starts long before the customer actually calls you with a question. Customer service is a combination of your marketing, your sales process, your product, and your educational materials. Only after all of those things have failed does the employee answering the phone come into play.