Suppress output from non-PowerShell commands?
Out-Null works just fine with non-PowerShell commands. However, it doesn't suppress output on STDERR, only on STDOUT. If you want to suppress output on STDERR as well you have to redirect that file descriptor to STDOUT before piping the output into Out-Null:
hg st 2>&1 | Out-Null2> redirects all output from STDERR (file descriptor #2). &1 merges the redirected output with the output from STDOUT (file descriptor #1). The combined output is then printed to STDOUT from where the pipe can feed it into STDIN of the next command in the pipline (in this case Out-Null). See Get-Help about_Redirection for further information.
A fun thing you can do is to pipe the output to Write-Verbose, then you can still see it if you need it by running your script with the -Verbose switch.
ping -n 2 $APP 2>&1 | Write-Verbose