I am looking for a website like flightradar24 but for trains, or I like to follow more precisely where my train is than the limited "next departures/arrivals" information that is readily available. Where can I find such information?
GRAPP Online map with all trains by Czech railway authority (SŽDC) Trains colored by delay. In details of train are scheduled and actual departures
Livemap via apps-bahn.de.
ndtv.com for all IR trains with NDTV
Actuele spoorkaart (in Dutch)
SJ Traffic Info. Can show the route and current position of a single train specified through the search box. Live position information is not available for all trains.
Realtimetrains. Detailed times but no map.
Raildar. Very roughly geographic diagrammatic representation. Tries to reconstruct how trains move through junctions between the reporting points in the raw data from Network Rail, but often fails miserably so can be confusing to watch,
Opentraintimes. More control-center style schematic presentation of the same data.
Traintimes offers live data of the London tube and via "More Information" in the upper right corner you can switch to London buses or National rail.
Traksy. Alternative presentation of the same data as Opentraintimes with an option to "track" a given train.
San Francisco Muni (choose "show map" after selecting line and direction)
San Francisco Muni (subway only)
Transit (app. Includes real-time location data for some urban and commuter services)
TRAVIC shows trains in many European countries, Australia, New Zealand, Japan, Indonesia, Israel, Brasil, Chile, USA, Canada; note though that for most trains the location shown is only interpolated from the timetable data. You can recognize a train for which live data is available by having a colored ring around the black ring (of the same color as the inner circle).