EDITED 8/31/2010 To clarify SQL Configuration Manager.

Below are three resources I came across that were very helpful troubleshooting remote connections via TCP and UDP to SQL Server 2008 Express. I have installed this on Server 2008 Foundation edition.

http://www.linglom.com/2009/03/28/enable-remote-connection-on-sql-server-2008-express/

http://www.sevenforums.com/system-security/58817-remote-access-sql-server-express-2008-windows-7-a.html

http://blogs.msdn.com/b/sql_protocols/archive/2007/05/13/sql-network-interfaces-error-26-error-locating-server-instance-specified.aspx?PageIndex=2#comments

In a nutshell:

• Enable TCP/IP connections via SQL Configuration manager.
• Blank out the dynamic portion for IP1 (IP46), IP2 (IPV4), IP4 (127.0.0.1), and IPAll and set TCP Port 1433. This was critical for me to get the system working properly.
  
• Make sure inbound and outbound rules (outbound rules are new to Server 2008) are added to Windows Firewall TCP 1433 UDP 1434.
• If you are behind a router/firewall and using NAT, make sure to ‘Allow Edge Traversal’ within the advanced tab of the rules you’ve created to allow incoming/outgoing traffic on 1433, 1434
  
  This was also critical for me to get the system working properly.
• Add SQLBROWSER.exe which is located in the x86 directory under 64 bit windows 2008
• For troubleshooting purposes one can use tcp: or np: in front of the server name to specify connection method (TCP or Named Pipe)

I have verified remote connectivity via SQL Management Studio 2008 and Toad For Sql Server 5.0.444 (Freeware)