Some of my apps that served me well in the past, such as GateGuru, seem out of date.
Looking for the most useful, well maintained ones.
I use Rome2Rio for travel between destinations and TripAdvisor for suggestions on top "things to do". Also, I like FlightView for tracking flights with real-time information so you can see where your plane is coming from and when it will arrive. I also have my airline and hotel apps.
For getting around and mapping I use CityMaps2Go and Google Maps. Having the apps for your particular airlines/hotels, especially if you are a frequent flier can make travel a bit easier (getting notifications of delayed flights, airport maps, checking into a hotel early, etc).
For flights: I have an app for each airline that I use. Also "Kayak" for checking flight times and prices.
For Trains: I have apps for the various train companies and also DB Navigator that has schedules for lots trains around Europe
Weather: "Dark Sky" It has good hour-by-hour forecasts and gives you rain alerts if it's going to rain hard soon
Restaurants: "Yelp" in the U.S. but more often than not, Rick's books in iBook or Kindle form on my iPhone in Europe
Things to Do: TripAdvisor
Driving/Transit directions: Google Maps. "Here" maps if I don't want to use data
Postcards: I use an app called "Ink" to send photos from my iPhone as postcards to my relatives that aren't as connected with Instagram, Email or Facebook
Currency: "XE" - It has a built in calculator that makes double checking how much I'm spending dead simple
Translate: Google Translate
I'm using a navigation app Spyglass that supports different maps, depending on my current needs: google maps, apple maps, open street map and open cycle map. It's also very important that the app can read pre-downloaded maps when offline. Besides, it has many useful features for those people that are not very good at orienting. The app shows your current position on the map, can save waypoints and locations, for example, your car or your hotel location. You can look it up here https://itunes.apple.com/app/spyglass/id332639548?mt=8&at=11lLc7&ct=fs
I like City Maps 2 Go - I pin all the places I want to see before going and then I can check when we are in certain ares to make sure I don't miss anything (awesome for pinning pastry shops...lol).
For noisy hotels/apartments, I like a white noise app - I have one called Sleep Pillow - I've had a few.
I love having a budget app to keep track of my spending - the one I have is just called 'spending', but I downloaded one called 'Spender' - haven't tried it yet.
Travelpod is great if you want to do a blog type thing. I always figure I will do it while away but am always too tired, so I'll just make notes about what we did each day and do it up when I get home. (NoteLedge and WordPress are also interesting, but I keep defaulting to Travelpod since it was the first I downloaded).
All these on my iPad...
I love the new app developed by a university called The Traveler. It's a way to track the path of everywhere you go, you can set down pins of points of interest, and you can sync it so that any time you take a photo out on your day, it'll pin it to the map and the path you've been on. Awesome for documenting your day!