Citymapper - The ultimate transport app - iPhone / Android / Web.
Tickey - Buy tickets for public transport with your smartphone
Embark - A public transport app that works everywhere
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.
Uber - Uber is a website and mobile app that allows you to get a ride similar to a taxi service from your phone.
TransSee - Real time transit prediction and bus tracker web app.