Search engine for OpenStreetMap data. You may search for a name or address(forward search) or look up data by its geographic coordinate(reverse search). Each result comes with a link to a details page where you can inspect what data about the object is saved in the database and investigate how the address of the object has been computed.
If you have large number of addresses or locations to add to a map, BatchGeocode can create a kml file. It uses a spreadsheet template to convert addresses to latitude and longitude so you can then map the points.