Google Adsense Publisher ID (or google_ad_client) is the only unique number that can distinguish your own Adsense code from another publisher's code. If an Adsense block is displayed with your publisher id on a site that you do not own, you will still receive the advertising revenue generated from that site because the code on that site is actually tied to your Google account via the Adsense Pub id.
When a site steals your Adsense code, you could make some extra money from someone else's content and traffic. But if you have been using Adsense for sometime, you probably know that this situation is certainly not the one to feel happy about even if you are making those extra pennies in the short-run. I say this for a couple of reasons:
» The Smart Pricing Phenomenon: If you are displaying Google Ads on a number of websites, even one low-performing website can cause Google to lower the ad prices (CPM) of all sites in your account. It's well know that only low-quality spam sites will copy your Adsense code and this could indirectly affect your Adsense earnings from existing sites. [more about Smart Pricing]
» Adsense Policy Violation: Google Adsense has some very strict policies with respect to the site content where you are planning to display the Google Ads. Imagine someone pasting your Adsense Code on a porn site - While Google will not ban your Adsense account for this immediately, you are sure to receive a warning for something which you havent' done.
» Adsense lets you create reporting channels for any custom URL. Visit the Adsense setup page and add new URL channels for all the sites owned by you where Google ads are being shown. Here's an example of URL Channels - one for a full website and another one for a blog hosted on blogspot.com
mydomain.com track all pages across all subdomains
myblog.blogspot.com track all pages across the 'myblog' subdomain on blogspot.com
Observe the page impressions for each of these channels and tally them with the results of your web stats package. If the page impressions from Adsense and the Page Loads from your analytics package are nearly same, you may not have to worry further.
However if the Site PageLoads is much less than Adsense PageImpressions, it's time to shoot a mail to Adsense support.
» Google recently introduced a new feature called Site Diagnostics available from the Reports tab of your Adsense control panel. This page has information about pages that Google has blocked from displaying ads due to a variety of reasons. If you see any page here that's not owned by you, send that information to Google immediately requesting them to stop serving ads on that page with your ID.
Also, it's very likely that someone copied-pasted the entire HTML code from your site to his own site without realizing that he is copying the Adsense ID also. In any case, this is just a form of website plagiarism and you can deal directly with their web hosting company to get the offending site removed forever.
I would still want Google to provide an option to Adsense publishers to specify a list of websites or blogs where they intend to display Google Ads just to be on the safe side always.
Notify Google about invalid clicks or related issues.
Here's the Google Official response on what Adsense publishers can do to prevent sabotage - "Google utilizes both automated systems and human reviews to monitor clicks on the ads. Google's technology analyzes clicks to determine whether they fit a pattern of invalid use intended to artificially drive up an advertiser's clicks or a publisher's earnings...In addition, you can review your site's traffic logs for suspicious activity and notify us with any findings."