Google Search
That's right, my next important iPhone app is one from Google. It's the bread-and-butter search app but also integrates Google Now. There are cards that show you things like flight info, and I love the way the search is so contextual. (Ask "Who is Barack Obama?," get the answer, then ask "How old is he?" and Google Now will know who you mean.)
AroundMe
I've been relying on this app more as I've been traveling lately. What I like most is the interface. You can find places around you like gas stations and hotels. There's one quick list of categories and the app uses location services to find points of interest. And if you've ever been in the situation of scrambling to find a place to stay at 2 a.m. after a flight cancellation, you'll appreciate the no-fuss approach. When you drill into the info, there's a summary, links, and photos to help.
Sprout Social
I've mentioned Sprout Social a few times before. As you can guess, this social media manager is the one I use to create a post that I then send to multiple services (and multiple accounts on those services). I can also quickly scan through tweets, mentions, and direct messages.