How do I output text without a newline in PowerShell?

Unfortunately, as noted in several answers and comments, Write-Host can be dangerous and cannot be piped to other processes and Write-Output does not have the -NoNewline flag.

But those methods are the "*nix" ways to display progression, the "PowerShell" way to do that seems to be Write-Progress: it displays a bar at the top of the PowerShell window with progress information, available from PowerShell 3.0 onward, see manual for details.

# Total time to sleep
$start_sleep = 120

# Time to sleep between each notification
$sleep_iteration = 30

Write-Output ( "Sleeping {0} seconds ... " -f ($start_sleep) )
for ($i=1 ; $i -le ([int]$start_sleep/$sleep_iteration) ; $i++) {
    Start-Sleep -Seconds $sleep_iteration
    Write-Progress -CurrentOperation ("Sleep {0}s" -f ($start_sleep)) ( " {0}s ..." -f ($i*$sleep_iteration) )
}
Write-Progress -CurrentOperation ("Sleep {0}s" -f ($start_sleep)) -Completed "Done waiting for X to finish"

And to take the OP's example:

# For the file log
Write-Output "Enabling feature XYZ"

# For the operator
Write-Progress -CurrentOperation "EnablingFeatureXYZ" ( "Enabling feature XYZ ... " )

Enable-SPFeature...

# For the operator
Write-Progress -CurrentOperation "EnablingFeatureXYZ" ( "Enabling feature XYZ ... Done" )

# For the log file
Write-Output "Feature XYZ enabled"

Write-Host -NoNewline "Enabling feature XYZ......."

While it may not work in your case (since you're providing informative output to the user), create a string that you can use to append output. When it's time to output it, just output the string.

Ignoring of course that this example is silly in your case but useful in concept:

$output = "Enabling feature XYZ......."
Enable-SPFeature...
$output += "Done"
Write-Output $output

Displays:

Enabling feature XYZ.......Done