Debian uses udev. Udev handles mapping MAC’s to the appropriate /dev/eth(X) file. If you copy a Virtual machine, Udev will remember the MAC address of the old NIC. When you copy the machine, the virtual host usually generates a new MAC address for the VM.
Udev will assign the new Device to eth1, eth2, and so on. If you want to change your NIC assignments make Udev forget the old MAC.
In Debian 5 (lenny) it is in this file:

/etc/udev/rules.d/70-persistent-net.rules

In Debian 4 (etch) it is in this file:

/etc/udev/rules.d/z25_persistent-net.rules

To apply changes in Lenny: “udevadm trigger” or “udevtrigger” (in Etch)