I would use either Get-Host or $PSVersionTable. As Andy Schneider points out, $PSVersionTable doesn't work in version 1; it was introduced in version 2.

get-host

Name             : ConsoleHost
Version          : 2.0
InstanceId       : d730016e-2875-4b57-9cd6-d32c8b71e18a
UI               : System.Management.Automation.Internal.Host.InternalHostUserInterface
CurrentCulture   : en-GB
CurrentUICulture : en-US
PrivateData      : Microsoft.PowerShell.ConsoleHost+ConsoleColorProxy
IsRunspacePushed : False
Runspace         : System.Management.Automation.Runspaces.LocalRunspace

$PSVersionTable

Name                           Value
----                           -----
CLRVersion                     2.0.50727.4200
BuildVersion                   6.0.6002.18111
PSVersion                      2.0
WSManStackVersion              2.0
PSCompatibleVersions           {1.0, 2.0}
SerializationVersion           1.1.0.1
PSRemotingProtocolVersion      2.1

PowerShell 7

The accepted answer is only appropriate if one version of PowerShell is installed on a computer. With the advent of PowerShell 7, this scenario becomes increasingly unlikely.

Microsoft's documentation states that additional registry keys are created when PowerShell 7 is installed:

Beginning in PowerShell 7.1, the [installer] package creates registry keys that store the installation location and version of PowerShell. These values are located in HKLM\Software\Microsoft\PowerShellCore\InstalledVersions\<GUID>. The value of <GUID> is unique for each build type (release or preview), major version, and architecture.

Exploring the registry in the aforementioned location reveals the following registry value: SemanticVersion. This value contains the information we seek.

On my computer it appears like the following:

Path                                                                                           Name              Type Data
----                                                                                           ----              ---- ----
HKLM:\SOFTWARE\Microsoft\PowerShellCore\InstalledVersions\31ab5147-9a97-4452-8443-d9709f0516e1 SemanticVersion String 7.1.3

As you can see, the version of PowerShell 7 installed on my computer is 7.1.3. If PowerShell 7 is not installed on the target computer, the key in its entirety should not exist.

As mentioned in the Microsoft documentation, the registry path will be slightly different dependent on installed PowerShell version.

Part of the key path changing could pose a challenge in some scenarios, but for those interested in a command line-based solution, PowerShell itself can handle this problem easily.

The PowerShell cmdlet used to query the data in this registry value is the Get-ItemPropertyValue cmdlet. Observe its use and output as follows (note the asterisk wildcard character used in place of the part of the key path that is likely to change):

PS> Get-ItemPropertyValue -Path "HKLM:\SOFTWARE\Microsoft\PowerShellCore\InstalledVersions\*" -Name "SemanticVersion"

7.1.3

Just a simple one-liner.

I needed to check the version of PowerShell and then run the appropriate code. Some of our servers run v5, and others v4. This means that some functions, like compress, may or may not be available.

This is my solution:

if ($PSVersionTable.PSVersion.Major -eq 5) {
    #Execute code available in PowerShell 5, like Compress
    Write-Host "You are running PowerShell version 5"
}
else {
    #Use a different process
    Write-Host "This is version $PSVersionTable.PSVersion.Major"
}

This is the top search result for "Batch file get powershell version", so I'd like to provide a basic example of how to do conditional flow in a batch file depending on the powershell version

Generic example

powershell "exit $PSVersionTable.PSVersion.Major"
if %errorlevel% GEQ 5 (
    echo Do some fancy stuff that only powershell v5 or higher supports
) else (
    echo Functionality not support by current powershell version.
)

Real world example

powershell "exit $PSVersionTable.PSVersion.Major"
if %errorlevel% GEQ 5 (
    rem Unzip archive automatically
    powershell Expand-Archive Compressed.zip
) else (
    rem Make the user unzip, because lazy
    echo Please unzip Compressed.zip prior to continuing...
    pause
)

I tried this on version 7.1.0 and it worked:

$PSVersionTable | Select-Object PSVersion

Output

PSVersion
---------
7.1.0

It doesn't work on version 5.1 though, so rather go for this on versions below 7:

$PSVersionTable.PSVersion

Output

Major  Minor  Build  Revision
-----  -----  -----  --------
5      1      18362  1171

EDIT

As of PowerShell 7.2.5, you can now do:

pwsh -v

Or

pwsh --version

Output

PowerShell 7.2.5

I have made a small batch script that can determine PowerShell version:

@echo off
for /f "tokens=2 delims=:" %%a in ('powershell -Command Get-Host ^| findstr /c:Version') do (echo %%a)

This simply extracts the version of PowerShell using Get-Host and searches the string Version

When the line with the version is found, it uses the for command to extract the version. In this case we are saying that the delimiter is a colon and search next the first colon, resulting in my case 5.1.18362.752.