I spend a serious amount of time using my three mobile devices. My current setup is a Samsung Note3, a 4th generation full size Ipad, and a reasonably new Dell Lattitude laptop. I also have a trusty Windows PC I built around 5 years ago which still gets a tonne of use. At this point I'm going to focus on the apps for the phone and tablet but you'll see that many are also available via webapp (usually via the Chrome Web Store).
This first batch is the basics....these are useful for all expats regardless of what country you're headed to or already at. I personally think these are excellent for anyone.
1) World time buddy - Basic (free) - Pro $4.00
One of the major downsides of working in the Asia Pac region for a US company is dealing with the difference in time zones. We're never at work when they are at work and vise versa. Add to this many don't take the time to figure out time zones so I end up with meeting invitations at 3 in the morning or just comments like "What is the time there?"
World time buddy takes world clocks to a new level in that it shows you on a clever grid format up to 4 time zones for the free version and up to 10 per group (I haven't run out of groups yet) for the pro version. The tool allows you to select a time in your zone (or any zone for that matter) and see immediately what time it is in the rest of the world. I personally think it's an indispensable tool.
2) XE Currency converter (Free) - Pro $2.00.
If you're changing countries, you're dealing with multiple currencies and need to be able to convert them. This, besides being by a Canadian company is the best I've found. I spent the whopping 2 bucks for the pro version which eliminates the adds and allows more currencies to be tracked.
On this point I suggest read about converting currency
here if you don't have a plan or you plan to use your bank
3) Lastpass - requires 12 dollar per year subscription for mobile use (free if you don't want it on your phone)
Lastpass is my soapbox app. That is I get on my soapbox and tell everyone I can about it. Lastpass handles every single password I have on every device I have extremely securely. At current count I have 233 passwords - every one is different, and intensely secure (Lastpass will create them for you if you choose). The only one password you have to remember is your Lastpass master password. The ones you want extra secure can be set so Lastpass asks again for the Master password.
Lastpass is actually free if you just want to use it on browsers on a PC, Laptop or IPad and then you pay $12 per year to have access on your mobile phone (as well as other helpful features).
Lastpass also has Secure Notes. These are password protected notes you can save within your Lastpass vault. You're an expat now, and as such have new country tax numbers and other funky data. Create a Secure Note for them and they are always at your disposal with your master password. You can even add attachments to your secure notes.
In Android Lastpass is also now filling in username and password in Apps. In both Android and iOS they have created their own browser which works well and auto populates user names and passwords into your websites.
In Windows - Lastpass has browser extensions for Chrome, Explorer and Firefox which work flawlessly. This is one of my can't live without applications.
4) Any decent cloud storage app - Dropbox is my favorite (free)
You're moving. That means you have more documents to fill out and sign and send than you can shake a stick at. You also have travel documents and it's a really really good idea to have scans of them available to you at all time. Enter the cloud storage app. I choose Dropbox as my favorite but Google Drive, Microsoft Onedrive, and Box.net are all good solutions and there are many more.
When we were moving I created a folder in dropbox to contain all of the many many documents. Real estate, moving, visa submission, job contracts, expenses, taxes, policies, insurance, and much more. I have dropbox installed on my PC, my laptop, my Android mobile and my iPad. When I put any file into a dropbox folder on any one device it synchronizes to all of the devices and can be accessed by any computer anywhere in the world at the dropbox website with the correct user name and password.
When you're doing one of these moves this accessibility is unbelievably convenient.
I personally like dropbox because it can natively read all of the major file types without needed other applications in both Android and iOS. Dropbox give you up to 2GB free and then you can buy additional space or earn it through a number of methods. Lately buying a Samsung android device has provided around 50GB for two years.