I wanted to include both English and Japanese body copy in my publication. However, I cannot read Japanese, and wanted to ensure I was presenting it in the correct way. Obviously if text is read from right to left, then alignment of text would be different. Below is what I found out:
Vertical Japanese is top-to-bottom, right-to-left; and historically (i.e. pre-WWII), horizontal text was treated as a single row of vertical text. This meant that since you start on the right when reading vertically, you started on the right here as well. Most of the time this was restricted to places where text didn't really fit well vertically (e.g. over/under images). Since WWII this usage has been replaced with writing horizontal text the same way Western languages write horizontal text, i.e. left to right (because, unlike with scripts like Arabic, you don't have to modify the actual letters in any way).
As a result, with extremely few examples, any example of right-to-left horizontal text you'll see in modern Japan is either historical or historically-flavoured (or period-correct, if it appears within fiction). You'll see it if you look at images from prewar Japan, though (a good example might be propaganda posters).
Japanese is not the only language that has done this, pretty much any writing system derived from Chinese did the same thing (for example, a good deal of Chinese temples have signs across the entrance written right-to-left).
Luckily enough, I can align Japanese body copy in the same way as I can for our alphabet system, as the language is now Westernised.