Every host on a network has down time, from the coolest RaQ to the lowest NT 486. The job of keeping down time to a minimum falls to the system administrator.
Various solutions are available, spanning the range of needs and budgets.
A solution at the other end of the cost spectrum is running a backup server which is manually switched with the primary server when necessary. In this scenario, if a server fails unexpectedly, it can be many minutes or hours before the poor system administrator can make the switch. This solution is both inelegant and widely used in company networks. Very interesting efforts are underway to offer completely Linux-based server clustering solutions. These include the open-source Linux Virtual Server, and other work being done by the High Availability Linux Project.