Safety
A dirty burner doesn't burn the gas properly. That can release carbon monoxide, which you can't smell or see. At every service we measure the flue gases. Put a CO alarm near the boiler too, it costs a few tens of euros.
Less gas, fewer breakdowns
A clean boiler uses a few percent less gas. And most of the breakdowns we fix in January, we could have seen coming at a service in September.
Warranty
Many manufacturers only give their full warranty if the boiler has been serviced every year. So keep the reports safe.
