Why do central banks in most countries create a serial number for every currency notes?

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Having serial number on notes is a type of accounting to keep track of all the paper money issued into circulation by the central banks. 

If there were no serial numbers, it would be hard to know how much money supply is out there. It also helps to keep fraudulent activity low. There are some websites which will allow you to track the paper currency and give a history about its use. 

The law enforcement agencies can also investigate certain financial crimes because only certain banks print a certain set of serial numbers. So, any counterfeit money out there can be identified and taken out of circulation.