How long will you be able to rent the movie?

You have 30 days to start watching, and once you begin, you can watch as many times as you want in 24 hours.

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from http://www.apple.com/appletv/

As it is a streaming service, the item will just disappear from your list.

lzylong said:

How long will you be able to rent the movie ? And after what will happen? it will just disappear?

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In the US:

You have 30 days to start watching the movie, after you start you have 24 hours in which to complete watching the movie or watch it as many times as you like. Once that period expires it is deleted from the HDD or, if I understand the new AppleTV correctly, is no longer available to stream from iTunes.

Everywhere else:

Same thing but you have 48 hours to finish watching the movie.

Note: TV show rentals are US-only for the time being and have a 48 window on them rather than 24 hours.