Sitecore patch configuration to add _basetemplates to the default Lucene index. Includes sample report.

BaseTemplateReport.ps1

$index="sitecore_master_index"

$props = @{
    Parameters = @(
        @{ Name="Info"; Title="Index"; Value="The report will be based on $($index)."; editor="info" },
        @{
            Name="searchBaseTemplate"
            Value=""
            Title="Base Template"
            Tooltip="Index the _basetemplates field as shown here on <a href='https://github.com/SitecorePowerShell/Console/issues/424' target='_blank'>Github</a>."
            Placeholder='{7B76036F5E-CBCE-46D1-AF0A-4143F9B557AA}'
            Mandatory=$true
        }
    )
    Title = "Base Template Report"
    Description = "Choose the criteria for the report."
    Width = 450
    Height = 300
    ShowHints = $true
}

$result = Read-Variable @props

if($result -eq "cancel"){
    exit
}

$database = Find-Item -Index $index -First 1 | % { $_.DatabaseName } 
$root = Get-Item -Path (@{$true="$($database):\content\home"; $false="$($database):\content"}[(Test-Path -Path "$($database):\content\home")])
$data = @{
    Index = $index
    Criteria = @(@{
        Filter = "DescendantOf"
        Value = $root
    })
}

if($searchBaseTemplate -and [Sitecore.Data.ID]::IsID($searchBaseTemplate)) {
    $data.Criteria += @{
        Field = "_basetemplates"
        Filter = "Contains"
        Value = ([Sitecore.Data.ID]::Parse($searchBaseTemplate).ToShortID().ToString().ToLowerInvariant())
    }
}

Find-Item @data | Show-ListView -Property Name, Language, Version, Url, Path -Title "Base Template Report"
Close-Window

Cognifide.PowerShell.Lucene.Index-7.config

<!-- Use with Sitecore 7.0 to 7.1 -->
<configuration xmlns:patch="http://www.sitecore.net/xmlconfig/">
  <sitecore>
    <contentSearch>
      <configuration>
        <defaultIndexConfiguration>
          <fields hint="raw:AddComputedIndexField">
            <field fieldName="_basetemplates" storageType="yes" indexType="untokenized">Sitecore.ContentSearch.ComputedFields.AllTemplates, Sitecore.ContentSearch</field>
          </fields>
        </defaultIndexConfiguration>
      </configuration>
    </contentSearch>
  </sitecore>
</configuration>

Cognifide.PowerShell.Lucene.Index.config

<!-- Use with Sitecore 7.2 and 8 -->
<configuration xmlns:patch="http://www.sitecore.net/xmlconfig/">
  <sitecore>
    <contentSearch>
      <indexConfigurations>
        <defaultLuceneIndexConfiguration type="Sitecore.ContentSearch.LuceneProvider.LuceneIndexConfiguration, Sitecore.ContentSearch.LuceneProvider">
          <fields hint="raw:AddComputedIndexField">
            <field fieldName="_basetemplates" storageType="yes" indexType="untokenized">Sitecore.ContentSearch.ComputedFields.AllTemplates, Sitecore.ContentSearch</field>
          </fields>
        </defaultLuceneIndexConfiguration>
      </indexConfigurations>
    </contentSearch>
  </sitecore>
</configuration>