Since the average home PC user does not have their Windows license in a place for easy access, I would say you would be severely limiting your business if you required seeing the license for every repair.
While I am not a lawyer, if you do nothing to add illegal software, or do not suspect that the PC has illegal software on it, you probably are not responsible for policing each PC you service.
If you suspect that another shop is installing illegal copies of Windows, then it might be in your best interest to take a close look at PCs that were purchased from that shop.
As far as re-installing Windows, that is a trickier issue.
First, you cannot pull the CD key from the registry for all versions of Windows.
Plus, for XP, you need to re-activate after a re-install.
Second, for each version of Windows, there are several distributions. To use the customers product key, you need the same distribution CD. Otherwise, you will need to use your key, and then change the registry back to their key.
For W98SE, there are 4 distributions that I have, and the product key for each does not work with the other CDs.
OEM Full, OEM update
Retail Full, Retail update
For W95, there are even more versions as their were 4 different OEM releases.
Then, there are the name brand systems that come with restore CDs and restore partitions.
There was a lengthy discussion in the Discussion Center on the related topic of finding evidence of illegal activity on a PC you were repairing.
The conclusions were mixed.
However, it was felt that the repair shop was not obligated to, and should not specifically look through the software and files on the PC beyond what was necessary for the repair work.
As with any business related legal issue, you should consult with your attorney as to what to do.
Chas