Duh, right? Instagram allows you to get your work out there and in front of people's faces. The most challenging thing about Instagram is to not let the number of followers you do or don't have affect you. Free for both iOS and Android devices.
Google's Snapseed gives you a more controlled mobile editing system than Adobe's Lightroom app. You can do the usual stuff like crop and lighten, but it also gives you in depth features like spot removal and dodging and burning! I highly recommend it! It's free for iOS and Android devices.
3. The Photographer's Ephemeris
Long name, handy app. It tells you when and in which direction celestial events like sunrise/moonset and everything in between will be happening. Did I mention that it also shows you a topographical map of the location so you can "see" what the light will look like at any given time? Freaking awesome! This app isn't free, however. I purchased it for $8.99 for iOS.
4. Camera-specific WiFi app
Hardy-har, but I have a Canon 6D, which has built-in WiFi. That means I can use it to view photos and download them to my phone, or use my phone as a shutter release. It's pretty dang rad, if I say so myself. I know Nikon and other brands may have apps like this, so if your camera has WiFi, be sure to look into it!
It's the moment all photographers dread: your gear gets stolen. If you use Lenstag, you can record all of the serial numbers of your gear, as well as their used/new value, so you can have it ready for your police report and insurance claim. Lenstag also runs searches on your serial numbers to make sure your images don't end up on sites you didn't authorize! It's available on both iOS and Android devices FOR FREE! You'd be foolish not to sign up.