Getting Application pools along with SharePoint sites with Powershell

[Void][Reflection.Assembly]::LoadWithPartialName("Microsoft.Web.Administration")

$sm = New-Object Microsoft.Web.Administration.ServerManager

foreach($site in $sm.Sites)
{
    $root = $site.Applications | where { $_.Path -eq "/" }
    Write-Output ("Site: " + $site.Name + " | Pool: " + $root.ApplicationPoolName)
}

Without powershell

http://sharepointchick.com/archive/2011/10/29/finding-the-application-pool-account-for-a-web-application.aspx