tubemap.live animates every train on a network across its schematic map, live. Positions are estimated from each operator's public data feed and interpolated between updates, so a marker can drift a little from where the train really is.

London Underground

Live data
Arrival predictions from the TfL Unified API. Train positions are reconstructed from each train's predicted arrival times along its route. Powered by TfL Open Data.
Map
The London Underground route map by Wikimedians (Wikimedia Commons, CC BY-SA 4.0).

New York Subway

Live data
The MTA's GTFS-Realtime subway feeds (all seven).
Map
The NYC subway diagram from Wikimedia Commons (CC BY-SA).

Hong Kong MTR

Live data
The MTR Next Train API on DATA.GOV.HK. The feed predicts arrivals rather than tracking trains, so individual trains are inferred from platform predictions.
Map
The Hong Kong network map from the Rail Map Toolkit community's rmp-gallery (GPL-3.0), drawn with Rail Map Painter.

Berlin U + S-Bahn

Live data
BVG's HAFAS endpoint via the community v6.bvg.transport.rest API: one trips query returns every running U-Bahn and S-Bahn train.
Map
The Berlin U- and S-Bahn map from rmp-gallery (GPL-3.0), drawn with Rail Map Painter.