1) Banks can be highly unpredictable
Sometimes banks can be a little unpredictable in the sense one cannot be sure. One individual recently recounted how a bank sent a letter to him despite his loan being complete. This can happen many years after the loan is complete and a letter can appear from nowhere. It's therefore best to take an NOC from the bank.
2) Cibil report
Sometimes there maybe a wrong report that is punched in or erroneously entered in your Cibil Ratings, regarding a loan that has been completely settled. A proof in the form of a NOC that the loan has been settled will hold you in good stead. This will ensure that your Cibil ratings reflect realty and you continue to remain creditworthy.
3) Legal proceedings
There have been cases where customers have received letters to face legal action, if they do not settle their dues. This is even after the dues had been settled earlier. An NOC helps you if there are any legal claims against you.
4) Notify the bank in case of change of address
We cannot always blame banks. Sometimes customers change their address and do not notify the bank. At other times they simply do not bother to collect the NOC.
In any case it's important that you take an NOC from the bank, once your dues are cleared. You do not want to regret at a later stage.