As a cyclist, I often need to measure the distance between two locations to have a rough idea.
The OSM website contains no ruler, and I was wondering if there were a way to add one, or if a similar site exists that does have one.
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It is easy enough to create a new web map application that does what you need. I would start with the OpenLayer's Measure Example and change the base map and extent to be the area of interest.
However, as far as I know ORS does not support worldwide coverage yet. Check the OSM wiki for more information (http://wiki.openstreetmap.org/wiki/OpenRouteService respectively http://wiki.openstreetmap.org/wiki/Open_Source_Routing_Machine).
For more routing engines/websites based on OpenStreetMap data check this wiki post.
"Sammys Fullscreen Map" does have a measure function on the left side:
more leaflet measure controls include (link to their demo pages at github)
You can also try BRouter web service which is specialized on bike routing.
Click on the map to define starting point and end/intermediate points, and you will get distances on real ways instantly.