There are a number of travel apps for the iPhone that I find very useful.  Of course there are many more, but these are the ones I use most.  

The Holiday Inn App is excellent, especially if you travel for work.  If you enable location services, it will give you options of all Holiday Inns near you, giving you the cost, availability and hotel information.
If you have a flexible booking, you can do a one click cancellation. And booking via the app is so much quicker than using their full website.  Another time-saver is the ability to store your corporate discount code within the app, so you don’t need to manually look it up and enter it each time you book.
Cost:  free
Drawbacks:  I think you first need to set you profile up through the full website before you can log in via the app.

I don’t live in London, so I don’t have the London Underground tube map etched into my brain, like most Londoners do.  So I use the Tube Map App when I travel to London.  I generally just need to use the map itself, but it has other good functionality: 
– Route planner with status updates & line information
– Notifications which can be configured, 
– Link to Oyster and @TfLTravelAlerts twitter feed
Cost:  free
Drawbacks:  None that I can think of

Skyscanner is a fantastic app for searching for cheap flights. It searches a range of providers including scheduled and cheap cost airlines.  But their USP (unique selling point) is that you can save searches and re-run them periodically to see whether there are any recent deals or price reductions.
I would say that it is probably one of the easiest and simplest apps I have ever used.  Searching for cheap flights can be an extremely onerous task, but Skyscanner has definitely taken the pain out out of the process.
Cost:  Free
Drawbacks:  Economy flights only.  Cannot search for premium economy, business or first class flights.

Google Translate has helped me out of many a sticky situations.  Whilst we were in Albania, we wanted to write a local shop-keeper a thank you note for  going out of her way to help us.  She had no English (or German or French or Afrikaans or Zulu or Spanish or Dutch – all the languages we could get by in), so we used Google Translate to write a quick thank you note.  Also used in China to communicate with our taxi driver as we needed to give him a specific instruction.
All the languages I have ever needed are available.
Cost:  Free
Drawbacks:  You need to be online to use it.  So again, be very careful if you need to use mobile data rather than wi-fi as it can get very expensive abroad!  Always try to buy data bundles at home before travelling or get a local sim card if you’re travelling for longer. It is certainly worth it!

The Metrolink app for Manchester’s tram system was also developed by mxdata, the same people who developed Tube Map above, so the look and feel is very similar.  It isn’t quite as sophisticated as Tube Map, as it doesn’t have all the bells and whistles that the London version has, but all the core functionality is there:
– Tram map
– Line status
– Route planning

Cost:  free
Drawbacks:  None.  Does what it says on the tin.

Duolingo is a fun app that either helps you learn a language, or at least practise it.  It has quite an ambitious purpose:  the people who developed it want users to ultimately help translate the worldwide web!  But on a more functional note, there are a number of levels you need to move through.  Each level introduces new words and combines verbal and typed exercises.  If I had kids learning French, German, Spanish, Portuguese or Italian, I would encourage them to register for this fun app.  When I have a spare few moment, I try and maintain some of my French, by using it.
Cost:  free
Drawbacks: there are only 6 languages (incl. English) available at this time.