Embark - A public transport app that works everywhere
Citymapper - The ultimate transport app - iPhone / Android / Web.
Uber Transit - Uber now offers real time data for public transportation
Google Maps - Find local businesses, view maps and get driving directions in Google Maps.
Moovit - For people that use public trasnportation a lot, or who rarely use it but need to on occasion, it can be difficult at times to figure out where you need to be to get where you need to go. Read more about Moovit.
Trenitalia - Italy train services official app