My answer seems to differ from most people here.
I do all sales and support once per day, first thing in the morning, getting the mailboxes to completely empty. I then glance at the mailboxes a few more times during the day, but don't send any more replies till the next morning. The only exception is if there's an urgent issue or serious bug.
This works for me because:
* I can concentrate on productive work (building new features) most of the day without serious distraction. If I were to reply to emails all day long, I'd get far less done.
* In my experience, users put that little bit more effort into solving problems themselves, if they're given the motivation to do so. They read documentation and FAQs. If you reply to emails within half an hour, you'll often find yourself in a lengthy back-and-forth that takes up a lot of time.
This second point might sound like heresy in a world where the customer is always right. But it's not so bad to lose customers whose opportunity cost in time is greater than their revenue is ever going to be worth.
While a small minority of users are unhappy to wait more than an hour or two for a reply, a guaranteed 24 hour turnaround is still pretty good compared to large companies.