Strava (Wikipedia) is a website and mobile app (for Android and for iOS) used to track athletic activity via GPS. Its headquarters are located in San Francisco CA. Most popular activities tracked are cycling and running/hiking. "The Strava dataset is growing by over 3 million activities a week and already contains 400 billion gps data points." 
Use of OpenStreetMap
Strava is introducing use of OpenStreetMap gradually, replacing google maps. They are using a "terrain" style rendered and hosted by Mapbox.
- Static maps (the small thumbnail map images) both on the web and within the mobile apps have used OpenStreetMap since early 2014
- Slippy maps on the web have switched from Google Maps to OpenStreetMap mid 2015. Slippy maps in the android and iPhone apps may not be switched yet.
- Routing, and the "route builder" is based off OSM data.
Strava's website of it: http://labs.strava.com/heatmap/
Data Permission - Allowed for tracing!
OpenStreetMap users can use Strava heatmap data for tracing into OSM only. For all other non-personal uses, including tracing into other datasets, please contact maps -at- strava.com.
The data is available on a purchasable license basis, so it is great that Strava allows the data to be used free of charge for the purposes of improving OpenStreetMap (similar agreements exist with aerial imagery providers).
- The Strava heatmap has been added to the JOSM presets, and can be activated through the preferences. (Imagery)
- Strava Slide iD fork gives access to these GPS tracks.
- For osm.org's iD: You could paste those URLs into the "custom" entry (only one possible) of the background settings:
Currently there are tiles in 8 colours available:
color8 (that may change).
If you have question regarding editing with the heatmap, please ask at for example help.openstreetmap.org (search for old, similar questions before). If you run into technical issues with these addresses (e.g. server/DNS error), please mail email@example.com
Routing Error Reports
Routing errors reported by Strava users can be viewed on a slippy map that has OpenStreetMap as a base layer. This could be used as a "check list" for mappers to investigate potential problems and correct them based on usual sources (like checking the location on-the-ground). http://labs.strava.com/routing-errors/
Strava have an API. Most of the information available relates to a specific user or their friends and so requires login through a Strava account. http://strava.github.io/api/
- Gpslib.ru - active since 2007; more functional counterpart, allows you to download traces with timestamps