I went through the process of enabling SSL on our SharePoint 2010 website.  However, whenever I tried to use it I would be presented with a login screen.  I was using the farm admin UserID so I knew it had authority.

I was able to find the following Microsoft document: You receive error 401.1 when you browse a Web site that uses Integrated Authentication and is hosted on IIS 5.1 or a later version
I already had the DisableLoopbackCheck registry entry, so I tried Method 1 and it worked great:

Method 1: Specify host names (Preferred method if NTLM authentication is desired)

To specify the host names that are mapped to the loopback address and can connect to Web sites on your computer, follow these steps:

1. Set the DisableStrictNameCheckingregistry entry to 1. For more information about how to do this, click the following article number to view the article in the Microsoft Knowledge Base:
   281308  Connecting to SMB share on a Windows 2000-based computer or a Windows Server 2003-based computer may not work with an alias name
2. Click Start, click Run, type regedit, and then click OK.
3. In Registry Editor, locate and then click the following registry key:
   HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Lsa\MSV1_0
4. Right-click MSV1_0, point to New, and then click Multi-String Value.
5. Type BackConnectionHostNames, and then press ENTER.
6. Right-click BackConnectionHostNames, and then click Modify.
7. In the Value data box, type the host name or the host names for the sites that are on the local computer, and then click OK.
8. Quit Registry Editor, and then restart the IISAdmin service.

I have been wanting to setup a non-www host header for our external websites and found that there are 2 steps to get this working:

1. Setup an Alternate Access Mapping in the default zone that specifies the domain without the “www”.
2. Manually add the host header to the IIS properties of the website.