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Each time I try cloning a perfectly working VM, the cloned VM has no internet connection. Is it a bug? I have changed nothing in the clone. When I try using the original VM, it connects to the internet just fine.

You can only "clone" HDD images. How did you clone your VM? I suspect that in creating the new VM, it of couse has a different MAC address. In this case you need to clear the udev rules file so that it pick up the "new" card with the new MAC address as eth0. There are lots of posts on this; here's one: http://forums.virtualbox.org/viewtopic.php?t=10569

You're right, I just cloned the HDD image. I have also deleted the udev file and generated a new MAC address. Started the VM and it made no difference.

You don't delete the file; you delete a couple of entries. What does ifconfig -a give you?