New York: PATH (4-subway/commuter lines), New Jersey Transit (Electrified Railroad, some trains stop in Newark, second busiest in North America), MTA Long Island Railroad (Busiest Railroad in North America, Electrified), Metro-North Railroad (4th Busiest in North America, most of the system electrified), Amtrak (Northeast Regional and Acela express. Theoretical commuting between Philadelphia and Boston, Electrified, Busiest long-distance railroad in North America)
London: London Overground (Basically the GO system we're envisioning but better because level boarding and stuff), Thameslink (Electrified), Crossrail (Under Construction, Electrified), Southeastern Rail, etc.
Here's the full list for London from Wikipedia:
Arriva Rail London, Caledonian Sleeper Chiltern Railways, East Midlands Trains, Eurostar, Gatwick Express, Great Northern, Southern, Thameslink, Grand Central, Great Western Railway, Greater Anglia, Stansted Express, Heathrow Connect, Heathrow Express, Hull Trains, London Northwestern Railway, South Western Railway, Southeastern, TfL Rail, Virgin Trains (West Coast), Virgin Trains East Coast
Granted, most of these are intercity trains, however, many stops are made in London.