I appreciate the old shows, too, and I have listened to quite a few of the old radio plays. I especially like the mystery and suspense ones! There are actually quite a few "Old Time Radio" podcasts out there. The one I subscribed to doesn't update any more, but there are tons of back-episodes to download.
I don't know about modern radio plays, though. I guess in the age of TV soap operas the radio play is going the way of the dodo. Although...I did listen to the kids' radio show Adventures in Odyssey quite a bit when I was younger. Despite being a kids' show the writing quality and production quality are astounding.
Otherwise I am starting to listen to some audiobooks on my ipod. They can be spendy, but if you get the download versions of older releases you can get them relatively cheap.
Oh, and if you're into the genre, there's a guy doing a "
Cthulhu Podcast" featuring works of HP Lovecraft and other scary stories set in and around the 20s.