Berlin Travel Guide This is a great travel guide for Berlin including an offline map of the city. It has sights, activities, shopping, restaurants, nightlife, day trips, and more. Very useful!
Öffi - Public Transport Buddy This amazing app has all the public transportation info for a stunning number of countries. Great interface, lots of ways of viewing the info - and works really well for Berlin.
Berlin City Guide This is an offline guidebook to Berlin - it has both hidden gems and mainstream interests - activities, sights, tours, food and drink, nightlife, shopping, and more. Also includes an offline map. Crashes sometimes.
Berlin Townster - Freizeit App If you can understand and read German, this app is great for finding fun things to do in Berlin, discounts, coupons, and places to be social. You can search by venue or type of venue.
Berlin Photos A collection of hundreds of photos of Berlin which you can use as wallpaper or share with friends in a variety of ways.