I wanted to share these websites/apps, which are probably useful for a lot of people. Is there something missing or something you want to add?
Maps
OpenTopoMap - same as above, Topographic map, has contour lines
Waymarked Trails - Hiking - Hiking trails, “clickable”, .gpx Download, background can be changed to OpenTopoMap
Waymarked Trails - Cycling - same as above for cycle ways
OpenSeaMap - free nautical database
OpenRailwayMap - the worlds railway infrastructure on one map
OpenCycleMap - map made for cyclists, highlights cycle routes and pubs
CyclOSM - a map style that highlights routes for cyclists and shows you the surface of the roads you ride on
Flosm - search through informations (opening hours, telephone number…) of a lot of POIs on OpenStreetMap, see list on the left
F4 map and OSMbuildings - both show map in 3D
Traze - see public transport in realtime, clickable, uses open data from public transport services
WheelMap - shows the wheelchair accessibility
Historic Maps - a map that combines OpenStreetMap with Wikipedia, shows historic objects and old maps as overlay
uMap - save markers, lines and shapes on different map styles, example: Map from /r/Castles
ÖPNV-Karte - a visualisation of the mapped public transport in OSM
Apps (all work offline)
OsmAnd - very advanced but strange GUI, shows public transport and hiking symbols, opening hours, etc, has routing, downloads offline wikipedia articles to objects, Android and iOS (less functions)
Maps.me - fast, easy tool, no hiking tools, elementary routing, free, Android and iOS
Locus Map - different map sources (also non-OSM like SwissOrdonance), has routing, Android only
OSMScout - GPS app with routing and social functions for Ubuntu Phone, Windows Phone, Android and iOS
OruxMaps - Map and sports tracker, can also connect with different bluetooth devices, Android
Gaia GPS - app for hikers, with search for trails and worldwide satellite and topo maps (offline only for premium users)
Poor Maps - OSM-based navigation for Sailfish OS
List of apps for Android and iOS
Routing Services
OpenRouteService - car, cycle and pedestrian routing with a lot of options, shows surface and type of used roads
Brouter Web - fast router,shows height profile, where routing table can be changed by yourself
Kurviger - a route planner that prefers curvy roads and slopes, but avoid cities and highways, automatic round trips based on a given length
Cycle.travel - a map made for cyclists, which has a routing and roundtrip feature, created by /u/doctor_fegg
Trail Router - routing app for runners, that favours green spaces and nature over the shortest path. It can generate round trip routes as well as point-to-point routes
FacilMap - planning tours collaborative with multiple map sources and elevation profiles
Printing OpenStreetMap Maps
MapOSMatic - printable atlases and single paper up to A0, lot of different map styles and overlays (like Waymarked Trails), free
Field papers - create an atlas yourself with different map styles,
Inkatlas - different styles, up to 6 pages A4 for free
Advanced/Other OSM based services
StreetComplete - small android app that makes it easy to add missing informations like surface, speed limits or cycle ways
Overpass Turbo - web based data mining tool for OpenStreetMap, linked is an example for cycle shops in Berlin
MapCompare - compare different map sources (Google, OSM, Here, Satellite data) with each other
WeeklyOSM - a blog about news in the world of OpenStreetMap
Mappa Pro - create your own small maps and share them
OpenInfraMap - view of the world’s hidden infrastructure (power lines, petroleum and water)
Mapillary - an open-source Streetview-Version you can contribute to
Peakfinder - shows all all surrounding peaks from the given point also available as app
OpenFireMap - map with all the fire houses and hydrants in OSM
Node Density - How dense is the OpenStreetMap database?
OpenStreetMap Wiki - Wiki of the OSM project