KML

KML stands for Keyhole Markup Language. It is an open standard now overseen by the Open Geospatial Consortium (OGC), but it originated as the native format of Google Earth — originally Keyhole Inc., hence the name. KML is an XML format. KMZ is a KML file archived with Zip compression.

Showing a KML layer over OpenStreetMap:

Simple KML viewing

• Quelltextlich's OSMTools KML example (corresponding wizard)
• UMap lets you create a map and then import a KML file (up-arrow icon on the right)

Developing for your own site (Javascript APIs)

• OpenLayers Dynamic KML
• Leaflet requires plugins to add KML support

OSM data in KML format

• Query-to-map
• OSM in Google Earth
• Map overlays for Google Earth

KML data into OSM

It might make sense to take KML formatted data and import it into OpenStreetMap. However, note the import guidelines. Probably it makes more sense to display the KML data in an editor and add the data manually.

• JOSM/Plugins/OpenData adds support for KML files to the JOSM editor.
• Potlatch 2/vector background layers feature supports KML as a format
• Merkaartor also supports loading in KML as a layer
• Converting to GPX format using GPSBabel or GpsPrune would yield a file which can be loaded into JOSM

See also Question:How to import KML files into OpenStreetMap?