I have kept/logged the serial numbers and game/machine number on all my dmd machines for a few reasons.
It is just interesting to see in the production run, where your machine was made. ie- at the beginning, middle or end obviously. But, it also is interesting to see if the first machines were made for the USA or Europe/Australia market etc.
With my Batman Forever Data East machine, for example, it was made in the last few days of the production run (apx 20 machines before the last one) and was a Aussie delivered machine etc. Some interesting info like that can be established from game numbers/serial numbers.
I also have a Tales From the Crypt which was sent to China of all places, and apparently, only a few were. Game numbers or production serials can turn up all sorts of interesting information.