Yes, I'm aware that Dropbox is less of an app than it is an online storage system, but that's precisely the point I made in my first post: the ability to transparently store your data in a way that is accessible everywhere changes every workflow. Dropbox was the first widely-available system that provided ubiquitous access to your files anywhere, and it does so completely transparently: from your perspective, your files are in a folder and sub-folders on your various devices. They are in the same place on every device. I have Dropbox on my Macs, my client PC, my iPhone and my iPad. My files are always at hand. The set-up is straight forward. Go to Dropbox, set up an account, be sure to use 2-factor authentication, and download the app for your Mac or PC, and install it. When you do, it will create a Dropbox folder in your home directory. Anything you put into it -- including both folders and files -- will sync to the Dropbox in the cloud, and sync to any other devices tied to the same account.
If you carry mobile devices, download Dropbox to them, as well. Now, your files are available anywhere you have any of your devices.
Dropbox Differences on Mobile Devices
By default, Dropbox on a Mac or PC syncs every file and folder on the device to and from the cloud. By default, Dropbox on a mobile device syncs none of the files and folders, but provides access to them through an Internet connection. Dropbox provides ways of changing this behavior, but the functions are different in the two environments, and you will have to decide how you want to interact with files and how much storage you want to set aside for them.
PC and Mac
Dropbox syncs your entire Dropbox to your PC and Mac, setting up a complete replica of the cloud version of Dropbox on your system. Given that most computer systems have sufficient disk space, this makes sense. However, there may be files or folders that are more archival or otherwise do not need to be always on your computer. If so, you can use Dropbox's "Selective Sync" feature (within the Account section of Preferences) to remove some folders and/or files from those that are always on the computer. Note that you can still access those folders using a web browser to Dropbox.com, but they will not be on the computer as local files, and won't be available when they computer isn't on the Internet. All other files will be available when you're offline, and will sync with the Dropbox cloud when you get back online. Dropbox handles conflicts smoothly, and uses icons and messages to communicate about the sync status.
On mobile devices, Dropbox works exactly the opposite: no files or folders are stored on the device by default. Instead, all interaction is by using an Internet connection through the Dropbox app. If you want a file to be locally cached (so that you can read it while on a plane, for instance), mark it as a "Favorite" by touching the star. This will cache the file on your device and also put the file into the Favorites section of the app.
More and more apps on iOS (and Android) interact directly with Dropbox, providing for workflows that store files in Dropbox that are edited or otherwise used by other apps. One common use, for example, is as a drop location for email attachments, both sending and receiving. You can even use a browser to download or upload files at any time from any where, including a friend's computer.
I use Dropbox to store all of my files and data that isn't dedicated to one particular app on one device. I even store some of those in it. The fundamental advantage for me is that I have all of my files on multiple systems (my Macbook Pro, my Mac Pro, and even my client PC) so that I can recover the files if anything ever happens to Dropbox. And Dropbox has the files if anything happens to my devices.
So, as a result of this foundational characteristic, Dropbox is the first app/system in this series.
Don't forget to let me know in the comments or my email your thoughts on apps or workflows you'd like to see included.