Thanks for letting me know.

You were absolutely right – it was the 3d acceleration all along! I managed to find other drivers for my radeon card, reinstalled cinnamon, and everything now works like charm.
I agree that it would be nice to be notified about using the 2D-version – I actually had no idea that I was doing so.
Anyway, very glad that everything worked out. Thanks for your help!

Actually, I should be thanking you. When Bill O’ didn’t reply back, I assumed he had installed it wrong. When you asked the same question, I looked into what could be causing the problem.
I knew that Cinnamon ran on top of GNOME 3. I figured that the problem might be the 3D acceleration. This is why Unity was not available for some Ubuntu 11.10 users – the hardware support wasn’t there – and they got the GNOME Classic desktop.
Ubuntu has both a 3D accelerated Unity and a 2D version of Unity. The difference between the two is subtle: (1) when Dash is active, the Launcher icons are greyed out in the 3D version, (2) holding the Super (Windows) key down will popup a help menu in the 3D version.
I now suspect that some questions I got about the GNOME shell are also related to 3D hardware acceleration. Personally, I think it would be nice if GNOME would alert the user that they are running in 2D mode instead of 3D (much in the way Ubuntu 11.10 would warn users if they didn’t have the hardware to run Unity).

Thank you for your comment.
The problem is 3D acceleration. If you don’t have it, you get the “traditional” GNOME desktop.
I run my test setups under VirtualBox, install the Guest Additions, and enable 3D hardware acceleration. When I turned off the 3D hardwre acceleration, Cinnamon boots into the GNOME desktop.
So, if you are running Ubuntu under a virtual machine, you need to enable 3D acceleration.
If you are running directly on the hardware, then it is likely that either (1) you have no 3D hardware acceleration, (2) the hardware acceleration is insufficient, or (3) the vieo hardware is not fully supported by Linux.

Are you sure you selected Cinnamon from the login screen?
The icon should be an empty circle (I just noticed I have the wrong graphic in my article and will correct it promptly).
You can have as many desktops installed as you like, but you actually have to select it in order to use it.
Otherwise, I am not sure why the Cinnamon desktop wouldn’t come up.
[UPDATE 21-June-2012 @ 00:00]
The likely problem is that you don’t have 3D hardware acceleration. I was able toreproduce your problem when I disabled 3D hardware acceleration. Cinnamon then comes up as the “traditional” GNOME shell.

As far as I know, when you run Ubuntu live from a live CD, ceertain software drivers will not be available (these are the so called “restricted” software). They are “restricted” because they may contain code that infringes on patents or licenses.
When you install Ubuntu on your system, you can select to automatically install this software. It is on the second page of the installation procedure: Preparing to install Ubuntu, at the bottom of the screen, click the checkbox next to Install third-party software.
If you have already installed Ubuntu, you can still install this software by searching for ubuntu restricted extras in the Ubuntu Software Center and install from there. You can also install it from the command line using sudo apt-get install ubuntu-restricted-extras
Thanks for your comment and praise.