YouTube has many movies from major studios around the world available to rent and to purchase. You can find the complete collection of movies at youtube.com/movies.
Each movie rental has a specific rental period, which is indicated in the purchase window that appears when you click the price button on the movie information page. Typically you'll have 30 days to start the movie and 24 hours from the time you begin playback to finish watching, but the exact times will vary for each title.
If you purchase a movie, it's yours to keep and add to your collection. All of your rentals and purchases will show up on your Purchases page.