Rome2rio
Plan your trip by viewing all possible ways to get from point A to point B. View prices and travel times, as well as get links to flights and train tickets. This is possibly my favorite app when thinking about multi-stop trips, or when first considering a new location.
Skyscanner
Skyscanner searches tons of websites for the most cost-effective flight, hotel, and car rental options out there, then links you to the website where you can actually make your purchase. My favorite feature is the "Everywhere" option. You type in your departure location, add your trip dates (or select an entire month if you're more flexible), and add "Everywhere" as your arrival- Skyscanner lists places you can fly to in price order all over the world!
FlightStats
Check flight times, delays, gates, etc. for any flight. This is my go-to app when weather is bad to check on my flight, or when expecting guests.
Moovit
Like Rome2rio, Moovit helps you get from point A to point B. However, this app works better for daily commute, or traveling within a city. I use it when heading somewhere I haven't been before and deciding which public transportation to take, as well as for my daily commute- it gives you minute to minute updates on bus/tram/metro movement (meaning I can check from my apartment if I have time to stop for a coffee or not), and you can have it give you live updates, so can read having to pay attention to when it's time to get off the tram!
Rail Europe
Search for train timetables and routes within Europe, buy tickets, and save your travel itineraries from multiple carriers. This is a great app for finding routes as well as keeping your travels organized.
GoogleTranslate
This one is my lifesaver. I use it constantly to translate emails, or just look for words I need in Italian. You can even speak directly into the app and have it translate what you say! I have friends who speak another language than their boyfriend/girlfriend who swear that this is the key to a successful relationship.
Afterlight
A great app for quickly editing all of your beautiful travel photos. It has more options than the iPhone Photo editor or Instagram, and gives you options within the app to share directly to Instagram or Facebook.
Touchnote
A fantastic app for keeping in touch with family and friends! Touchnote lets you turn your own pictures into postcards and send them out directly. While the app itself is free, it does cost about $2.00, but that's about the cost of any postcard, and this way you can share your travels through your own perspective.
Expedia
Expedia is my go-to when searching for flights and hotels (others swear by Booking), but my favorite use for this is when I'm trying to be spontaneous. During both my "Go to the Train Station and Go Wherever" trip to Torino and my problematic "Go to the Train Station and Go South" trip to Rome, Pompeii, and Amalfi, I booked my accommodation from my phone through my Expedia app. I didn't end up staying anywhere fancy in Torino, Rome, or Amalfi, but I found somewhere relatively cheap and in great locations all three times- and checked in within hours of booking! It was also a lifesaver when I forgot to book my parents and I a place to stay in Stuttgart- again, we didn't end up staying in the best hotel we've ever been to (far from it), but Expedia saved the day for sure!