You can't actually save the background image onto your computer, as far as I know. There may be a way to find the folder that the backgrounds are stored in, rename them to .jpeg and then save somewhere.
Edit: Ok, I found out how to do it. It's quite complicated.
-------------Short way-----------------
Naviagate to:
C:\Documents and Settings\
<username>\Application Data\Microsoft\MSN Messenger\
<number>\Backgrounds\
Open the .DAT files in paint. Then save as PNG. You have now saved the background iamge onto your computer.
-------------Long way-----------------
Go to your Harddrive (Usually C:\), then Documents and Settings, double click your name.
Now, you need to go to Tools > Folder Options > View > tick 'Show Hidden Files and Folders'
Now, you should see 'Application Data' folder (below), double click it.
Now go into the 'Microsoft' folder, then the 'MSN Messenger' folder.
You'll find lots of folders with numbers. Start looking in them until you see a folder in them called 'Backgrounds'. It should look something like this:
Right click one of them, Open With... Paint. You'll have to do this with every one until you find the one you want. Once you have, save it as PNG onto your desktop.