If I rent a movie from iTunes can I watch it on the airplane with my iPad?

You can, if you have completely downloaded it to your iPad.

When u rent the movie, it will download to your computer. After you get it downloaded to your computer, make sure you have "sync movies" checked, then check the movie you want to Sync, press apply and it will Sync to your iPad. If you order it from iTunes on your iPad it will download to your iPad once you pay for it. Once the rental runs out, it will automatically remove from your device.

If you downloaded the movie to iTunes on your computer, you must move it to your iPad before you watch it (assuming you want to see it on your iPad).

If you download a rented movie on your computer: You can transfer it to a device such as your Apple TV (1st generation), iPhone, iPad, or iPod if it’s a standard-definition film (movies in HD can only be watched on your computer, iPad, iPhone 4 or later, iPod touch (4th generation or later), or Apple TV). Once you move the movie from your computer to a device, the movie will disappear from your computer's iTunes library. You can move the movie between devices as many times as you wish during the rental period, but the movie can only exist on one device at a time.

This is done through iTunes on your computer, and involves synching with your iPad.

See http://support.apple.com/kb/HT1657

Regarding ZintainUSA's response: be careful!

The movie will not co-exist on the computer and iPad. You must move it, as I described.

I never stated it would co-exist. I simply was giving the directions as to how to get it on the iPad.