Here's a factoid that will blow your mind: the Burj Khalifa -- the tallest building in the world -- is so large that you would be able to watch the sunset from the base of the building, take a lift right to the top and watch the sunset all over again.
In fact, if you are a Muslim living on top of the Burj Khalifa, you will have to fast longer during Ramadan because of this time difference: about three minutes between the time of the sunset on the ground and the sunset on the top.
You can experience this from every tall structure, however, provided that you have a fast-enough way to reach the top. You can even get the same effect on a calm day at the beach, with no help at all. First, lie down on the sand looking at the horizon. When the Sun completely disappears, jump as fast as you can. You will be able to see the end of the sunset once again.
The taller the structure and the faster you can get to the top, the longer you will be able to enjoy the second sunset. This happens because the Earth is curved, and by sticking out perpendicular to its curvature, you'll be able to see more of what lies behind the horizon.
Top image: the_dead_pixel/Flickr