The 2.2 software update is supposed to allow this. I have not tried it yet.

"iPhone OS 2.2 also brought a major new feature to both the iTunes Store application that users have been requesting for quite some time: on-the-go downloading of podcast episodes. Users can either start up the iPod app and tap "Get more episodes" to launch the iTunes Store on the iPhone, or simply go straight to the new Podcasts category in the store manually. Both video and audio episodes can be downloaded over WiFi or (surprisingly) the cellular network.

The feature is useful, but has its limits. First, podcasts cannot be subscribed to on the iPhone; you can manually download individual episodes to get a quick fix, but you can't create a new subscription or batch download 20 episodes and start binging. Second, the 10MB cap already in place for songs and applications is in effect, which means you'll have to connect to WiFi if you want to download anything larger. "
Source(s):
http://arstechnica.com/news.ars/post/20081121-lots-to-like-about-new-iphone...

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iPhone software release 2.2 supports the download of podcasts. I'm not sure how you would do that while on a plane, though... unless you can find one that already provides WiFi access.

Here is a link to an article about it: http://www.dvcreators.net/iphone/
Source(s):
http://www.dvcreators.net/iphone/

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As long as you've upgraded to the 2.2 firmware, then yes it does (same on the iPod touch)

Have a look at page 122 of this manual for more info - http://manuals.info.apple.com/en_US/iPhone_User_Guide.pdf

I don't believe there are any 3rd party applications available that let you download podcasts.
Source(s):
http://www.apple.com/iphone/softwareupdate/

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Check out the firmware 2.2 update -- it allows over the air (OTA) podcast downloading.
Source(s):
http://blogs.zdnet.com/Apple/?p=2458
http://www.iphonehacks.com/2008/11/firmware22-news.html

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