Over the past 6-7 years the use of remote support has grown enormously. As a matter of course all clients are immediately setup with VPN and remote support services for their Servers, Desktops, Laptops and Network hardware.
The way this is setup varies a bit, most companies will use the built in VPN service that comes with Mac OS X Server. This has been a reliable service in Mac OS X Server since Tiger and is doing just as well in Snow Leopard Server.
VPN is only part of it, Apple Remote Desktop is then used to gain access to the remote computers. Generally this is configured with security so that only authorised persons are allowed access or authorisation must be granted before the remote support person can take over.
Other ways to provide remote support include iChat, Skype, TeamViewer, LogMeIn and even using the built in iChat (Jabber) server included with Mac OS X Server. With iChat you are able to ask permission to share a computer without the need of VPN.
Sometimes remote support can fall short when handling Mac Servers but there are options that can be installed to make remote support better. Lights Out Management built into Mac Xserve can allow a remote user to turn the power on and off remotely. There are also remote power supplies that can be installed to turn off Tape Drives or anther hardware.
Some server work is best done over a remote connection and out of normal work hours. Much better to do this than getting everyone to stop working.
Generally Onsite Support is faster for deployments or serious server issues. For clients with a server problem usually a remote control would be attempted but failing that a visit will be arranged the same day and as soon as possible.