How to cat a UTF-8 (no BOM) file properly/globally

Create a file utf8.txt. Ensure the encoding is UTF-8 (no BOM). Set its content to €

In cmd.exe:

type utf8.txt > out.txt

Content of out.txt is €

In PowerShell (v4):

cat .\utf8.txt > out.txt

type .\utf8.txt > out.txt

Out.txt content is â‚¬

How do I globally make PowerShell work correctly?

Windows PowerShell, unlike the underlying .NET framework^[1] , uses the following defaults:

on input: files without a BOM (byte-order mark) are assumed to be in the system's default encoding, which is the legacy Windows code page ("ANSI" code page: the active, culture-specific single-byte encoding, as configured via Control Panel).
on output: the > and >> redirection operators produce UTF-16 LE files by default (which do have - and need - a BOM).

File-consuming and -producing cmdlets do usually support an -Encoding parameter that lets you specify the encoding explicitly.
Prior to PowerShell v5.1, using the underlying Out-File cmdlet explicitly was the only way to change the encoding.
In PowerShell v5.1+, > and >> became effective aliases of Out-File, allowing you to change the encoding behavior of > and >> via the $PSDefaultParameterValues preference variable; e.g.:
$PSDefaultParameterValues['Out-File:Encoding'] = 'utf8'.

For PowerShell to handle UTF-8 properly, you must specify it as both the input and output encoding^[2] , but note that on output, PowerShell invariably adds a BOM to UTF-8 files.

Applied to your example:

Get-Content -Encoding utf8 .\utf8.txt | Out-File -Encoding utf8 out.txt

To create a UTF-8 file without a BOM in PowerShell, see this answer of mine.

By contrast, PowerShell Core, the cross-platform edition of PowerShell, fortunately defaults to BOM-less UTF-8 on both in- and output.

^{[1] The .NET framework uses UTF-8 by default, both for in- and output.

This - intentional - difference in behavior between PowerShell and the .NET framework it is built on is unusual.}

^{[2] Get-Content does, however, automatically recognize UTF-8 files with a BOM.}