I don't know how I ever managed to catch a flight back before the Internet; actually, back before I could access the Internet from a small device that has more computing power than what sent Man to the Moon.
I love what that little box can put in my hand... Google maps, with my favorites pinned, and live bus, tram, or metro directions; Google Translate that lets you take pictures of a menu and actually read it, or TripAdvisor, or Yelp, for the skinny on restaurants and cafés.
While I may book with my laptop using Kayak, Expedia, Cheap Tickets, or Joe's deal of the day, I typically install the app to double check bookings during the trip.
But perhaps even more important to me are what I can the transient apps I get before a trip, I start loading up on apps that will be deleted within hours of my arrival back in the US... destination language aids, offline maps and tour guides, transportation apps, and so on. (I prefer the free apps, of course.)
But don't forget your airline app. You probably have the app for the airline you typically use, but what about for the airline that you will use for just one leg of your trip? You can use Air line apps to check in 24 hours in advance, of course, but you can often pull up terminal maps, watch streaming entertainment, get notifications, present your boarding pass, and most importantly: rebook a missed connection.