In Word versions up to 2003, the label definitions are stored in the registry in the following key
HKEY_CURRENT_USER\Software\Microsoft\Office\x.0\Word\Custom Labels
Where x.0 = your Word version (11.0 for Word 2003, 10.0 for Word 2002, 9.0 for Word 2000, etc.).
You can access the registry by typing regedit in the Windows > start > run dialog box and pressing enter.
If you are changing between Word versions, then it is wiser to simply write down the customized settings and re-enter them in the new version. I am pretty sure that Word 2002 and 2003 use the same configuration (albeit in a different registry key appropriate to the Word number) but Word 2000 and 2002 keys are incompatible. I don't know about Word 97.
Provided that the Word versions are similar you can export the registry key to a text file.
Select the custom labels key in the left window and pick file (or registry) > export (depending on the Windows version).
The registry editor will produce a text file similar to the following.
Windows Registry Editor
Version 5.00
[HKEY_CURRENT_USER\Software\Microsoft\Office\11.0\Word\Custom
Labels]
"Viking L14-100 2x7
A4"=hex:4c,03,5c,00,00,00,6c,00,5d,00,26,16,00,00,6b,08,00,\
00,1c,01,00,00,8b,03,00,00,b4,16,00,00,6b,08,00,00,02,00,07,00,01,00,02,00,\
00,00
"Viking L24-100 3x8
A4"=hex:4c,03,5c,00,00,00,6c,00,5d,00,2d,0e,00,00,c1,07,00,\
00,8d,01,00,00,fe,01,00,00,9e,0e,00,00,c1,07,00,00,03,00,08,00,01,00,02,00,\
00,00
This produces a text file - filename.reg - which you can select in Windows Explorer, then right click and Merge to incorporate into the registry.
The vast majority of popular label formats are included with Word as pre-configured templates.
If you however you use custom label definitions, this page shows how to transfer those definitions to other PCs.