There are lots of must have apps, it depends on the tastes and spheres you need and like:
Messengers Telegram, Whatsapp, Viber, Facebook messanger, hangouts.
Social Media Instagram, Facebook, Pinterest, Vimeo, GooglePlus, Twitter, flickr, etc.
Video/Music/Pics ArkMC, media player and streamer to playback or beam media that you have stored on PC, MAC any UPnP/DLNA server wirelessly.
Photo Lidow or VSCO, photo editors with free filters.
GPS MapsMe an offline map that can help you not to be lost in a world, just download a map you need (any country) and use it offline with the GPS navigation.
Docs Microsoft Office suite works really nicely on the big screen, which is especially important when you want to multi-task.
Seattle Freeways for traffic updates
Boggle for when I’m at church
Reeder to keep track of feeds/blogs
Ted Mobile for long drives
Pictureka for the kids and parents
Momento for passive journaling
ESPN Radio for NBA action on drive home
Instapaper for Techmeme and TechCrunch articles
ShopShop to keep track of grocery lists
Amazon Price Check to make sure I’m not paying too much
Track Weight to track. my. weight.
How Stuff Works for when you are bored but want to learn something
Google Maps – Google Maps, which was once included with all iPhones, is now an app that you have to download separately—and you should. Google Maps has proven itself more accurate than Apple’s own map app, with turn-by-turn directions by car, foot, and public transportation. With Google Maps, you’ll see estimated travel times, integration with your Google account for quick access to your home and work addresses (optional), and the ability to rotate the map by pressing two fingers to the screen and twisting them.
Google Translate – With more than 30 languages supported and the ability to deliver impressively accurate results most of the time, the Google Translate app is one of the most remarkable programs you can load onto your iPhone. Most people probably won’t need it too often, except when traveling or studying a language, but it can be amazingly useful in unexpected circumstances.
Flixster (also called Movies by Flixster, with Rotten Tomatoes) – Flixster isn’t just another movie- and theater-information app. Yes, it does list movies with ratings and plots and theater show-times, but it also offers some extras, such as Rotten Tomatoes ratings and social integration. It’s a clear, well-designed app that efficiently gets you the information you need to make your movie-viewing decisions and to easily purchase tickets. You can even watch movies right inside the app if you purchase them or already have them in your UltraViolet collection.
Photo Wallet – Great app allowing you to download your entire Flickr library. An awesome way to bypass the annoying iPhoto/iTunes method of getting photos on your phone. Your entire Flickr organizational structure is mirrored, and you can search by tag. It’s like having a digital asset management system on your iPhone.
Pastebot – essential utility; the clipboard Apple forgot. This app is incredibly slick, and also allows you to send text and images back and forth to your Mac.
Consume – elegant utility from Bjango allowing you to monitor your AT&T minutes and data, as well as Dropbox, Evernote storage allotments, mileage balances for a variety of airlines, and much more.