I am looking for a WMS layer for OSM to use in any GIS program (ARCGIS for example). I have seen it working but I am not able to retrieve a WMS URL by a google search.
Does OSM provide such a service?
No, OSM does not provide such a service. I made a search last week and found a few open WMS services. There must be more but you can have a try with these:
http://osm.omniscale.net/proxy/service?service=WMS&request=GetCapabilities (Germany)
http://osmwms.itc-halle.de/maps/osmfree?SERVICE=WMS&REQUEST=GetCapabilities&VERSION=1.1.1 (quite nice, but covers only part of Germany)
http://osm.prtr.bund.de/cgi-bin/mapserv?map=/data/umn/osm/osm_s_10k_opt_agg.map&VERSION=1.1.1&REQUEST=GetCapabilities&SERVICE=WMS& (also nice and also just part of Germany)
Both Geoserver and Mapserver show OpenStreetMap data on they web pages and making your own WMS service with Mapserver is quite well instructed in http://trac.osgeo.org/mapserver/wiki/RenderingOsmData
I haven’t found any example of Mapnik based WMS service yet.