Besides the apps the airlines put out to aid you with your flights (schedules, eta, etd, etc.), there are some apps you might consider using (based on availabilty to your location).
HopStop: Recently acquired recently by Apple so only available in the Apple Store. Helps you get from point A to point B using the local public transit.
Citymapper: Similar to HopStop but only available for London and NYC.
MetrO: Covers 400 destinations around the world in a more basic way.
Walkit: Covers UK for walking.
Uber: At the click of a button you can have a car come for you. Works in various world cities and is cashless – charges your card directly.
Pingspot: You can pin your favorite shops and restaurants. You can also leave a photo.
Flying: Keep track of your flights. Interact with friends throughout your journey.
iStone: Translation app designed for travelers without linguistic skills for the country you are in. 12 languages.
Packing Pro: Customize your own list so you don’t forget what you need.
Postagram: Make a personalized postcard from a photo. Works with your phone, Facebook or Instagram photos.
Photosynth: Another photo app but this one lets you take 3D and 360-degree photos.
Splid: Photo and audio app. Splid allows you to take pictures but not edit them so people can’t accuse you of “Photoshopping” something.
Minube: E-Library with thousands of user-generated mini-guides. Covers 24,000 destinations in 200 countries (and counting.)
These are just a few of the many travel apps out there.