Have I accidentally relicensed my key? I've just realised that when I duplicate my boilerplate Craft site to start a new client project, I haven't been deleting the license.key file as per the docs here. What are the potential problems here? Does Craft regenerate a key file if it's already used, or have I somehow licensed a single key multiple times?
You should have seen a warning that the license belongs to another domain (https://craftcms.com/support/license-transferring). 

If not; are these duplicate sites still on a non-public (development) domain? That might explain why you did not see the warning. In either case: simply delete the license file for the duplicate sites and Craft will create a new one. You might need to clear the caches as well.