Berlin's U/S-Bahns certainly give the impression of being open 24/7 -- I've never had problems getting to/from clubs or airports at any time of day.

London can also claim a useful 24/7 service, with the night tube starting a couple months ago and the third and fourth lines (Jubilee and Northern) just opening up this week[1].

[1]: https://tfl.gov.uk/campaign/tube-improvements/what-we-are-do...