I've seen such sites in the past.
I remember seeing one put together by Wm Lerer at a conference a couple years ago.
What I'm looking for is a map that demonstrates all (well, at least a lot) of the freely available basemaps (tilesets, web services, etc) that I could include in a mapping application (using OpenLayers, Leaflet, or whatever).
Best Answer
There is no organized catalog of XYZ tile servers per se. The closest thing is the leaflet-providers project which provides dozens of free basemaps. Code for integrating with leaflet is provided but it should be relatively easy to translate to OpenLayers or other mapping clients.