The ventilation a specific boiler requires depends on its size and efficiency. Larger boilers always require more robust ventilation, and some gains in efficiency depend on optimal air flow.
The combustion process, which creates the heat captured by water in boilers, needs heat, fuel and air; ventilation ensures that sufficient air is able to flow through the system. Having too little air can cause the combustion process to fail or operate inefficiently, while too much air can take heat away from the system and create undesired combustion by-products.
Gas- and oil-fueled boilers produce a small amount of gas that needs to be vented away and minuscule amounts of particulate matter. Wood and coal fuel, which produce far more gas and particulate matter, generally require more ventilation.