I was under the impression this was a killer feature of iOS5. I'm running the latest versions of OSX, iTunes and iOS.
iOS 5 does not do automatic Podcast download or subscription. OTA downloads are available only for Music, Apps and Books under the
For podcast management, you're still required to sync with iTunes. This might change in future versions, but it is not in the current version, nor can I find any references that it will be.
If your podcasts are automatically being downloaded by iTunes on your computer, you leave your iTunes running, and you have Wi-Fi Sync enabled, podcasts will be automatically synced to your iOS 5 device when it is charging.
This works great for me -- a computer with iTunes constantly running, and my iOS 5 iPhone 4 plugged in to the charger on my bedside table.
Doesn't quite answer your question, but there are a number of fantastic iOS podcasting apps that do download automatically over the air and let you stream podcasts as they download as well.
My favorite is Instacast. I've switched completely to using Instacast to manage podcasts. No more syncing to iTunes, no more managing podcasts, just subscribe and play. Can't recommend the app enough.
If you are downloading the podcasts to iTunes first - then you can set up your iPhone/iPad to over the air sync and, YES your podcasts can be included with that.
You'll need to leave iTunes running on your computer. Then either start the wireless sync manually on the iDevice (go to "Settings", choose "General", then click on "iTunes Wi-Fi Sync", and finally hit "Sync Now") or by setting up iTunes so that it automatically syncs when the device is plugged in to power. (then it just goes over the air when you plug it in)
Hope that's helpful.. Struck me that lots of the answers here implied 'no', but the answer is actually 'yes'.