Windows 10 is perhaps the most Internet-connected and cloud-centric operating system released by Microsoft to date. This, of course, has caused many users to be concerned about how the OS respects their privacy (or doesn't).

Multiple sources are now claiming that this OS reports user data to Microsoft which could be violating the users' assumptions of privacy. (A couple of examples are linked below.)

How legitimate are these concerns and claims? Is Microsoft actually collecting data about Windows 10 users' location and activity? Are they actually authorized to do so, simply by a user's acceptance of the EULA?

I'm aware that Windows 10 sends malware files to Microsoft for analysis. This is a common and generally-accepted practice for most antivirus products, and antivirus is known to be integrated into this OS. What about the other information?


TechWorm - Microsoft’s Windows 10 has permission to watch your every move
BoingBoing - Windows 10 automatically spies on your children and sends you a dossier of their activity


Microsoft Windows Pre-Release Preview (aka Windows Insiders) Privacy Statement,  January 2015: (no longer applies)

When you acquire, install and use the Program software and services,
Microsoft collects information about your use of the software and
services as well as about the devices and networks on which they
operate. Examples of data we may collect include your name, email
address, preferences and interests; location, browsing, search and
file history; phone call and SMS data; device configuration and sensor
data; voice, text and writing input; and application usage. For
example, when you:

install or use Program software and services, we may collect information about your device and applications and use it for purposes
such as determining or improving compatibility (e.g., to help devices
and apps work together),

when you use voice input features like speech-to-text, we may collect voice information and use it for purposes such as improving
speech processing (e.g., to help the service better translate speech
into text),

when you open a file, we may collect information about the file, the application used to open the file, and how long it takes to use it
for purposes such as improving performance (e.g., to help retrieve
documents more quickly), or

when you input text, handwrite notes, or ink comments, we may collect samples of your input to improve these input features, (e.g.,
to help improve the accuracy of autocomplete and spellcheck).



This is so serious that even some political parties here in France that have nothing to do with technologies denounced Microsoft Windows 10 practices.
A member claimed that the statement above does not concern the shipped version of Windows 10.
Well:

We have not been provided any proof that Microsoft removed all those monitoring modules of its Windows 10 beta version in the final release. And, since Windows is closed-source, there's no way for us to check ourselves.
The media has reported a history of Microsoft spying as its practice (e.g. Microsoft, China clash over Windows 8, backdoor-spying charges, also NSA Built Back Door In All Windows Software by 1999).
For the shipped version of Windows 10, we can see the same information with smoother words: Privacy Statement

Additionally, after the release of the shipped version of Microsoft Windows 10, this is what was written in Microsoft Windows 10 Privacy Policy:

We will access, disclose and preserve personal data, including your
content (such as the content of your emails, other private
communications or files in private folders), when we have a good faith
belief that doing so is necessary to protect our customers or enforce
the terms governing the use of the services,

Only by the start of this August, and after lot of organizations and even political parties complained about Windows 10 being a spyware, Microsoft changed its privacy policy statement to softer terms to which I linked to. But is this change of policy statement followed by retrieving Windows 10 from the market and replacing it by a new one? Of course not.
Note that the last paragraph I quoted is only still available in external websites including famous newspapers by the start of this August (which thing means after Microsoft started already to sell its Windows 10), but we do not find this paragraph anymore in the updated version of the privacy policy statement anymore. So Microsoft removed it already.
Update:
From Windows 10 feedback, diagnostics, and privacy: FAQ (shipped version of Windows 10, NOT Pre-Release Preview), we can also  read regarding Diagnostics Tracking Service:

As you use Windows, we collect performance and usage information that
helps us identify and troubleshoot problems as well as improve our
products and services. We recommend that you select Full for this
setting.

Basic information is data that is vital to the operation of Windows. This data helps keep Windows and apps running properly by
letting Microsoft know the capabilities of your device, what is
installed, and whether Windows is operating correctly. This option
also turns on basic error reporting back to Microsoft. If you select
this option, we’ll be able to provide updates to Windows (through
Windows Update, including malicious software protection by the
Malicious Software Removal Tool), but some apps and features may not
work correctly or at all.

Enhanced data includes all Basic data plus data about how you use Windows, such as how frequently or how long you use certain features
or apps and which apps you use most often. This option also lets us
collect enhanced diagnostic information, such as the memory state of
your device when a system or app crash occurs, as well as measure
reliability of devices, the operating system, and apps. If you select
this option, we’ll be able to provide you with an enhanced and
personalized Windows experience.

Full data includes all Basic and Enhanced data, and also turns on advanced diagnostic features that collect additional data from your
device, such as system files or memory snapshots, which may
unintentionally include parts of a document you were working on when a
problem occurred. This information helps us further troubleshoot and
fix problems. If an error report contains personal data, we won’t use
that information to identify, contact, or target advertising to you.
This is the recommended option for the best Windows experience and the
most effective troubleshooting.



Note that only on Enterprise Edition one can turn Diagnostics Tracking Service off totally.
Diagnostics Tracking Service available in Windows 8.1, Windows Server 2012 R2, Windows 7 Service Pack 1 (SP1), and Windows Server 2008 R2 SP1 and Windows 10. The quoted paragraphs concern the Diagnostics Tracking Service mechanism in which other modules, apart from Telemetry, are included.
Diagnostics Tracking Service consists in these files:

telemetry.asm-windowsdefault.json
diagtrack.dll
utc.app.json
utcresources.dll

Note that the answer below claiming that nothing private is collected by Windows 10 as a qualified user may listen to the traffic of his Windows operating system is wrong. It is impossible to know what Windows collects and sends permanently. Windows does not stop sending  information on his/her behalf as this study shows: Even when told not to, Windows 10 just can’t stop talking to Microsoft. But still what the official documentation describes is not very good for the user such as when Windows takes system files or MEMORY SNAPSHOTS, which may unintentionally include PARTS OF A DOCUMENT YOU WERE WORKING ON on when a problem occurred (From: What are the privacy and security implications of Windows Telemetry)
