Windows Server 2003 support is ending July 14, 2015. This KB article guides you to upgrade the Windows Server 2003 to Windows Server 2008 within a VM.
VMware vSphere ESXi 5.5
VMware vSphere ESXi 5.1
Read the following Microsoft KB to make sure all the requirements are met before starting the upgrade: Supported paths for upgrading from Windows Server 2003 to Windows Server 2008
Note: You might have to reboot the Guest OS several times during the upgrade