Exchange Server 2003/2000 do not have any built-in mechanisms for a "backup server". You can look at Microsoft Clutering Services (MSCS) or third-party solutions that provide database/storage and/or server redundancy.
<b>Dial-tone recovery:</b> A backup server may be as simple as having another Exchange Server running. When the first/production server faces an outage (generally an extended outage of the storage/Database requiring recovery from tape), you can resort to what is known as "dial-tone recovery". This involves "connecting" users to another Exchange Database, running on another server. Users get an empty mailbox with no old email when they connect - but it allows them to send/receive new messages. Meanwhile, the Database with the old email is recovered from backup media, and mailboxes merged with the "new" mailboxes.
<b>Recovery Storage Groups: </b> Take a look at Recovery Storage Groups. These allow you to restore a copy of a mounted Database to an alternate location, and extract data from it. <a href="http://technet.microsoft.com/en-us/library/aa998782%28EXCHG.65%29.aspx">Using Recovery Storage Groups in Exchange Server 2003</a>
Exchange Sever 2007 further facilitiates such recovery scenarios by allowing easier Database Portability and allowing users to be connected to a new mailbox database instantly using the shell.
<b>Server Failure and standby servers:</b> Another way of protecting against a server failure, without having to deal with clustered deployments is simply using an identical server with no drives as a standby. In case of hardware failure (except the Storage sub-system) of the production server, drives can be moved to the standby server and operation resumed in no time. This does not provide any protection from logical corruption of the Database or from a drive/storage sub-system failure.
Exchange Server 2007 raises the High Availability bar a lot higher, with built-in mechanisms like <a href="http://technet.microsoft.com/en-us/library/bb125195(EXCHG.80).aspx">Local Continuous Replication </a>(LCR), <a href="http://technet.microsoft.com/en-us/library/bb124521(EXCHG.80).aspx">Cluster Continuous Replication</a> (CCR), and <a href="http://technet.microsoft.com/en-us/library/bb676502(EXCHG.80).aspx">Standby Continuous Replication </a>(SCR, new in Service Pack 1).