Csdrhrt

Look at the file

C:WindowsSystem32License.rtf

Can be found for all these Windows operating systems

Vista, W7, W8, W8.1

These License rtf will have the Version of Windows and the Edition also, Windows 7 Pro for example.

Windows 10 has the rtf file but does not show edition, but if it has the arbitration clause note at the top you know it is W10, or use the explorer trick in Matthew Steeples answer.

Using the registry you can look up version and edition

I found this answer over at Stackoverflow to the question Determine Windows Version, Edition and Service Pack OF AN OFFLINE DISK IMAGE

Use the values under HKLMSOFTWAREMicrosoftWindows NTCurrentVersion. I presume you know where to find that hive?! The
respective hive can be found under %SystemRoot%System32config with
the name SOFTWARE.

Side-note: you can attempt to verify your results by looking at some
well-known files (e.g. kernel32.dll, ntdll.dll) and into their
version information resource (what you're looking for is the file
version: with, e.g. GetFileVersionInfo()).

Edition values, if that's needed, can be found at
HKLMSYSTEMCurrentControlSetControlProductOptions.

More specifically, how to load the hive of another registry:

http://www.microsoft.com/resources/documentation/windows/xp/all/proddocs/en-us/regedit_load_hive.mspx?mfr=true

If you can still run executables from that filesystem, you can run C:WindowsSystem32winver.exe

If you have Linux on the same system, you could boot into Linux, ensure the Windows partition is mounted (for instance here it's in /mnt/C) and then do strings /mnt/C/Windows/System32/ntoskrnl.exe 2>/dev/null | grep amd64. For me in printed 9600.18258.amd64fre.winblue_ltsb.160303-0600, and googling for winblue indicates that this was the code name for Windows 8.1.

Open the file bootmgr in notepad it is located on the hard drive you are wanting to know the version of it will be a hidden file so select show hidden files in folder options sorted

If you don't have a running Windows and want to find the information from a Linux machine, you can use hivexget to read the registry file on the disk.

For Debian-based systems, install it with sudo apt install libhivex-bin.

Example (with grep to make the output shorter):

# hivexget /mnt/tmp/WINDOWS/system32/config/software 'MicrosoftWindows NTCurrentVersion' 

| egrep 'ProductName|CSDVersion|"ProductId'

"ProductName"="Microsoft Windows XP"

"CSDVersion"="Service Pack 3"

"ProductId"="76487-OEM-0011903-00101"

Remove the | egrep ... part to see all values under that key.

Get Magical Jelly Bean Keyfinder. The portable free version works fine. Safest to get it from their website magicaljellybean.com or sofpedia etc.

Start it up. Under the tools menu, select >> load hive. It then shows all your drives, select the windows folder of the drive in question. It instantly provides the version and keys.