To support Web Farms (multiple machines) or Web Gardens (multiple processors), changes to the ASP.NET configuration will need to be made. Thankfully this is just configuration; no code changes would need to be made.
The main thing to be aware of when setting up for a farm/garden is that a user's request can hit any processor or server. As such, the user's session needs to be available across the entire farm/garden and so session state cannot be held locally in memory, which is the default configuration.
The following links give further details on what can be involved:
Session-State modes: http://msdn2.microsoft.com/en-us/library/ms178586.aspx
Web Garden Model: http://msdn.microsoft.com/library/default.asp?url=/library/en-us/dnaspp/html/dngrfTheASPNETHTTPRuntime.asp