Just to add, many of the companies that I have worked for have 24/7 support. Also, many of the smaller hosts that have dedicated servers through one of the companies I've worked for had a simple way of providing 24/7 support.
Basaiclly, they rely on the fact that it isn't something that most of their customers will use. What they did is included in their welcome e-mails a statement to the effect that they would appreciate it if customers would follow this type of escalation procedure for their questions:
1) Use the "self-help" resources that are provided (FAQ/KB/Tutorials/etc)
2) If that fails, to try asking in the forums
3) If that fails, to open a TT
4) If all else fails or its an important issue to call their toll free number
(again I'd have to recomend uReach.com for this service)
Basaiclly, they simply have the phone number routed to their cell phone which they leave on 24/7 and get awakened maby once every other week or so (if that). Providing it is much better than not - in fact, many have mentioned to me (as we resell uReach service) that they almost never receive tech support issues and simply get new customers "testing" whether or not it is actually 24/7 support.
Another possibility is an advanced phone system that redirects calls based on time of day - and they simply have a few friends with cell phones that work out a scheudle (helps if a few of them work a night/overnight shift at their day jobs).
A final possibility is to have an answering service (as opposed to voice mail) - that way, the customer has the impression of talking to someone, being able to vent and give their issue - and is simply told that we will look into the issue and get back to them once a resolution has been researched & tested (its little things like that one can use to give customers the impression that its 24/7 - even though you might not get the message until you wake up several hours later - but customers seem to like it).
Hope thats helpful....