I needed to add the custom Content Type (CT) “RDC_Link to Document” to all Libraries of sub-sites of a particular site.
My CT has already been created using the UI at Site Collection > Site Settings > Content Types
Running the below PowerShell code in the SharePoint Management Shell solved my problem.

$site = Get-SPSite http://intranet
$CTtoAdd = $site.RootWeb.ContentTypes["RDC_Link to Document"]
$Web = Get-SPWeb http://intranet/Web/
$Web.webs | ForEach-Object {
 $_.title
 $_.webs.lists | where { $_.BaseTemplate -eq "DocumentLibrary" } | ForEach-Object {
 #I used $_.Webs.Lists above to target the 3rd level down (i.e. http://intranet/Web/Web/Web)
 if($_.title -eq "Site Assets")
  {
   write-host "Skip Site Assets"
  }
  else
  {
   try
   {
    $ct = $_.ContentTypes.Add($CTtoAdd)
    write-host "Content type" $ct.Name "added to list" $_.Title
    $_.Update()
   }
   catch
   {
    write-host "Failed to add Content type" $ct.Name "to list" $_.Title
   }
  }
 }
}
$Site.Dispose()
$Web.Dispose()

If you wanted to add the CT on all Libraries in your Site Collection you would replace the first 5 lines to the following:

$CTtoAdd = $site.RootWeb.ContentTypes["RDC_Link to Document"]
$Site = Get-SPSite http://SiteCollection/
$site | Get-SPWeb -Limit all | ForEach-Object {
$_.title
$_.lists | where { $_.BaseTemplate -eq "DocumentLibrary" } | ForEach-Object {

To delete CT’s and for other ways to add them, check out this blog post