I have done a quick check-through in an attempt to find patterns. It differs from Japan, but there is some logic here. In many cases, the US codes are "identical" to their EU counterparts, just with extra stuff added.
For Europe, xxxx often becomes MK-xxxx-RR (MKxxxxRR) or xxxx-RR. The "RR" represents the Region Codes, in most cases it is 50.
SG-1000
Japanese product code rules. No change.
Master System
US and EU codes are identical in most cases, mostly due to identical publishers.
First Party:
I believe every first party game has its own code, but they don't always print it on the spine. However, I am of the impression it was incorporated into the barcode like this.
32kB ROM (Card) - 40xx
32kB ROM (Cartridge) - 45xx
128kB ROM - 50xx
Combo cartridges - 60xx
256kB ROM - 70xx
3D - 80xx
512kB ROM - 90xx
512kB ROM + backup - 95xx
Germany - 410xx - overrides everything for some reason
Third Party:
This applies to Europe only because there weren't really any third-parties in the US (Activision has its own rules).
Sega doesn't adopt the T-series stuff straight away. It sticks with MK-whatever-50. But it starts dealing with five number patterns instead of four.
256kB ROM - MK-27xxx-50
512kB ROM - MK-29xxx-50
note the "2".
Vitally important point - Brazillian boxes also degrade into a similar system - "02x.xxx". I don't quite understand it though.
Mega Drive
new system adopted.
At the beginning Sega don't bother to print codes on the spines at all, so this might be wrong. I think barcodes can offer clues.
First Party:
1xxx
ROM sizes may affect the second digit. I can't see a clear pattern if I'm honest.
Third Party:
T-xxxx - T-series code, essentially. Sometimes they drop the "T-", sometimes the "-50" for Europe. I don't know why. And this applies to everything Game Gear and Mega CD-related too
Game Gear
First Party:
2xxx
Mega CD
First Party:
4xxx
32X
First Party:
We jump for some reason to
84xxx
Third Party:
Third party codes change slightly. Just slightly.
In Japan, letters are added to the end, so for 32X it becomes
T-xxxxA
in the US/EU it is
T-xxxxB
T-xxxxB-50 being the European variant
Saturn
First Party:
81xxx
accessories at this stage are
801xx (US) and 803xx (EU)
Third Party:
In Japan we've moved forward to
T-xxxxG
in the US/EU it is
T-xxxxH
"what happened to the other letters" you might ask
Dreamcast
First Party:
5xxxx
Third Party:
In Japan we've moved forward to
T-xxxxM
so in the US it is
T-xxxxN
BUT in Europe, it is
T-xxxxD-50
these are initial findings, there may be anomalies. Presumably there is third-party software out there that is of the pattern T-xxxxC, T-xxxxE, T-xxxxF, T-xxxxI, T-xxxxJ and T-xxxxK


