Software for digital nomads

The three most important things you'll need are communications, collaboration, and travel. All these apps are free and I've provided links to the app inside the appropriate stores.

On your laptop

Evernote - make a note of anything, including photos, video and sound. It all gets synced with the cloud and available on all your devices. It has a fantastic search function. Put photos of all your valuable documents (passport, travel insurance, etc) in there for quick reference. Windows or Mac.
Google drive / Dropbox - backup files, share them with customers. Windows or Mac. Dropbox is available for Linux.
Slack - a chat room for teams including NomadList. Windows, Mac and Linux.
Skype - for meetings with customers. It's screen sharing function is really useful when you can't be physically present to show how to do something. Windows, Mac, iPad and Linux.
Speedify - a VPN that can multiplex several connections together to get more speed and/or reliability. 1GB of traffic is free each month so you can save it for days when internet is especially bad.
Backblaze - cloud backup that will Fedex you a hard disk containing your data if necessary.

On your phone

TripAdvisor - I use the "restaurants near me" function when I'm out and get hungry. If you're using the app for reading accommodation reviews it's better done on a laptop through the web. Android / iOS.
Wifi Analyzer - to find the place where the wifi network is strongest. Android or iOS.
Google translate - when you know the shop assistant won't understand the meaning of "band aid" but you really need them right away. Android / iOS.
Instagram - make those envy inducing snaps even envier! It optionally posts to Facebook and twitter at the same time, so it's really convenient and efficient. Android / iOS.
Currency converter - unless you convert local prices into 'your' prices, it's easy to spend a lot more than you intended to. $8 salad in Chiang Mai, I'm looking at you. Android / iOS.
Kindle - you don't need to go out and buy a Kindle device, access millions of books from the convenience of your own phone. Android / iOS.
Evernote - that shopping list you wrote on your PC will be there when you're in the supermarket. Android / iOS.
Trello - use trello.com to manage tasks and communication with your customers. The app on your phone will also help you keep on top of things and stay responsive. Android / iOS.
Uber - taxis for short or long trips. Android / iOS.
Grab - popular taxi app in Southeast Asia. It was there before Uber arrived, so there are more drivers available. Android / iOS.

If you need a phone number in your home country for customers to call, use Google Voice or SkypeIn. Skype can forward calls to your local number so you never miss a call and are always available. It's usually best to use the call forwarding function (which works over more stable and ubiquitous 2G) rather than installing Skype on your phone and then trying to use it over patchy 3G when out and about.

My most recommended app is using Trello for managing tasks with clients. The interface is incredibly simple, it's really powerful, and the app on your phone will save you over and over.

If you're going to Bali or Vietnam then you'll want some sort of VPN (optional, but helpful in Thailand) as some very useful web sites are blocked there.