There's been some confusion about what happens when you install SharePoint 2010 on a Domain Controller. To further complicate things, the behavior in the release version of SharePoint 2010 is exactly the opposite of what it was in the beta. It's like they're messing with us!
To clear it up; if you install SharePoint 2010 on a Domain Controller, you get a Server Farm (also called Advanced) install. You do NOT get a Single Server (also known as Basic) install. Heck, you don't even get the option to install a Single Server install in the UI. If you want one, you have to script the install using a config.xml file.
Now, that's confusing to some folks, because the public beta was exactly the opposite. If you installed the SharePoint 2010 beta on a Domain Controller, you got a Basic install whether you wanted it or not. And of course you didn't. My only guess is that in the beta timeframe they knew they wanted to force our hands on the install type, but somewhere a 1 got flipped to a 0 and the wrong option was installed. That's fixed on RTM though.
So why do they care? Well, it comes down to SQL Express, I think. If you do a Basic Install you get SQL Express as part of the deal. To install SQL express on a Domain Controller in a supported fashion you need to tweak some things during install, which are detailed here. The appeal of a Basic Install, if there is one at all, is that there's nothing to configure. So which route would they go then, not bother the user for the extra info and install SQL Express in an unsupported fashion, or break the sacred vow of the Basic install and prompt for information? They took option three, don't install SQL Express at all. Now, let's be clear on what "supported" means. "Unsupported" does not mean "won't install on" or "you're a freakin' super genius if you figure out how to do this." It just means it's not the intended way for the software to run, and Microsoft hasn't tested it. You can install SQL Express on a Domain Controller without setting all those settings, as the Beta install showed us. It just hasn't been tested, and may break somewhere down the line.
That's the story. Not much to it. Just wanted to clear that up a little.