It may be tempting to just let this slide as you can "earn a few dollars as well."
What's the catch?
If the other site violates the Adsense policies -- e.g. they click on the ads using your code -- you can be the one terminated
There is a setting under Adsense Setup called Allowed Sites where you list your allowed URLs. That way, Google knows that these are the sites where your income should be counted
There is a section underneath where Google will tell you where your ads have appeared outside of your allowed sites, so you can track easily who has stolen your code