My observation is that the "spaces" (now called "desktops") in Mountain Lion are sorted in a "most recently used" type order. That is, the more often a switch to a particular desktop, the closer to the "front" of the desktop list it is moved. If you enable the 4-finger "swipe up" Mission Control gesture, you can see the desktops in their "swipe" order.
I suspect one reason for this is that "full screen" apps get their own desktop, so the number of desktops varies dynamically, and the simple number/grid scheme from earlier OS X versions no longer can apply.
I tend to switch apps with command-tab, so the absolute placement of desktops is not so relevant to me. I do occasionally miss the ability to switch to a particular desktop with control-number, but have gotten used to using "swipe up" to find and select the desktop I want.
If you want to associate an app with a desktop of its own, switch to the "last" (empty) desktop, start the app, and select Options->Assign to This Desktop from the context menu in the dock for that app. If the app supports full screen mode, simply switch it to full screen and it will create its own desktop.
I was going to include a sample "Mission Control" screenshot below, but I haven't answered enough questions here yet, so I've posted it on dropbox instead. You can use the 4-finger left/right swipe to switch desktops in this view, or you can click on the thumbnail of the desktop you want to switch to. Across the top of the screen are the desktop thumbnails. Spotify is in full-screen mode. Desktop 4 has no apps on it. If I put an app there, I will get a new empty Desktop 5. I'm currently on Desktop 1, which is shown "exploded" below the thumbnails.