For gas and oil-powered boilers and water heaters, you need to select a venting system that will work in your home. Chimney vented units vent exhaust naturally through a chimney. Power vent and direct vent use fans to push exhaust through vent pipes and can usually be vented either vertically through a roof or horizontally through a sidewall.
The difference between the two is that direct vent units pull intake combustion air from outdoors and can be placed in any room, while power vent units use air from inside and can only be installed in open rooms and can not be put in tight closets or crawl spaces.
Some boilers and a select few water heaters have a condensing style venting and are highly efficient. These units however, have special venting requirements due to the acidity of the condensate they produce.