I really am not a productivity app sort of guy. I have a lot of games, but most apps strike me as just dedicated browsers for someone's web site. To date I am a big user of the Kindle app and the Feedly RSS feed reader app and the Gmail app. Oh, and Google maps (the Apple maps program still sucks). And that is about it.
But I have been using Tripcase (free) to bring together all my travel info and I really like it. All one has to do is forward airline, hotel, car rental, restaurant, etc confirmations to a certain email address and the program parses out what information it needs. The only work is that each confirmation gets set up as a separate trip, but it is easy to merge three or four together to get all of one trip in a single record. It provides a nice interface with travel information and provides notifications for such things as flight delays and gate changes.