Short answer:

Play them via Avatron Air Sharing.

Longer answer (an iTunes FAIL):

I wanted to watch the “Using UDK” video tutorials that 3D Buzz has made available to teach people the basics of the Unreal Development Kit.  The iPad makes it pretty easy to watch these videos while I run on the treadmill.  All the videos were in MP4 format, so I reasoned that my iPad could both play them.

I was in a hurry, so I used Air Sharing to upload one of the videos to my iPad so I could watch it where I was going.  Then, I tried playing the video through Air Sharing’s interface.  It worked great.  Woohoo!

Now, it’s important to note that for whatever reason, it didn’t occur to me to use iTunes to get the video onto the device.  That turned out to be serendipitous.  Thinking that it would take too long to upload all the videos via Air Sharing (because I was unaware that Air Sharing exposes itself as a network share onto which could drop these videos), I imported all the videos into iTunes and tried to sync them to the iPad.

iTunes reported that none of the videos were of a suitable format for the iPad.  WTF?

Doh!  The iPad must have some different kind of support for MP4, I thought.  Unsatisfied with that, I downloaded Air Sharing onto the iPad and repeated the process described above.  And it worked.  Mind you, Air Sharing doesn’t use a special player; it invokes the QuickTime player built into the device.

So WTF iTunes?  Why are you telling me a video is incompatible with the iPad when Air Sharing demonstrates that the device is perfectly capable of playing it?

Apparently, for each file it’s asked to sync to a device, iTunes makes a summary judgement regarding its compatibility with the device.  But it’s judgement is wrong.  Maybe it’s looking at the file’s data rate or resolution or some metadata indicating that it wasn’t converted via the wondrous iTunes video converter and is therefore not worth attempting to copy.  Whatever the case, iTunes refuses to transfer videos based on an arbitrary rule, not because the file in question is actually incompatible.

This is a cardinal fail.  An old proof-of-concept video game—Façade—did this same thing to me long ago.  Everything I said then remains true, here.

So why might the iTunes devs have gone this direction and prohibited me from viewing these videos on the iPad?  (Yes, they’re prohibiting me, because the iTunes conversion process is not a fast or reliable option; the converter didn’t even produce a usable video when tested.)  It’s a philosophy of first impressions: Apple reasons that it’s better to prohibit any use of an “unknown quantities” like these videos than risk the poor market perception that might otherwise result.  Say, for instance, that iTunes did permit me to sync any video to the iPad, and that when I tried to play it the iPad struggled, dropping frames or playing stuttering audio.  Further assume that the video in question simply is beyond the capabilities of the device; let’s face it, the iPad is powerful but it ain’t that powerful.

The average user won’t know anything about video data rates, compression, codecs, or reasonable expectations about hardware’s performance.  All the average user will see is the iPad not doing what they expected it to do.  When lots of users have this experience, then a market perception will have emerged that could damage the iPad’s sales.  (And Apple would have to field a lot more support calls.)

So in this case, Apple’s choice is clear: don’t risk the poor perception.  Then, the only question is how to avoid it.  Because there are way too many variables in play to make a conclusive decision about whether a video might play well or not, the makers of iTunes had to adopt arbitrary performance criteria based on educated guesses—anything that satisfies the arbitrary criteria is permitted, and anything that doesn’t  is prohibited.

That’s not good enough.  There are advanced users out there, and some of them use Apple products.  They like to be able to click the magic “Advanced…” button that grants them the final word on how criteria-driven features like this should behave.  But iTunes has no such button, and so the advanced users post blogs about why the product failed to live up to their expectations.