There are three reasons to shoot with your camera in the horizontal (landscape) orientation.
First, because of the side-by-side arrangement of our eyes, shooting wide reflects the way we see.
Second, because the standard of shooting wide was established by Thomas Edison in 1909 and maintained since then even for TV, viewers are used to seeing movies that are wider than tall. Starting in 1952 with the advent of Cinerama, the ratio has varied, but the idea of wider than tall has prevailed. You can find a concise history of aspect ratio here.)
Third, and most important, playback conventions used by YouTube and other video hosts assume that the video was shot horizontally. If you upload a vertically shot video and then play it back from the Internet, the image will be smaller on your screen, with black bars filling in the unused space.
You can see what we’re talking about by comparing two amateur clips of a landslide in China. The material was featured in The New York Times. The first frame, taken with a camera held horizontally, fills up the space. The second frame, shot with the smartphone held vertically, has black vertical bars, which were imposed by the playback software.
If you intend to show your movies only on your phone, you won’t have the black-bar problem. But if you want to exhibit your videos widely—whether on the Internet or in theaters—shooting horizontally will almost always give you a professional look.
Of course, there is no law about aspect ratios; it’s just a matter of convention. Some filmmakers, for example, have chosen to exploit the strange look of vertical shot video for comic effect. Simon O’Neill’s “Tell Me About Yourself” is a delightful example.