The words I've covered on Twitter for the past 2 days are:
お化け おばけ obake - Ghost (informal, less serious term)
幽霊 ゆうれい yuurei - Ghost (more formal term)
呪う のろう norou - to haunt; 呪われる のろわれる norowareru - to be haunted
Two famous anime ghosts: おばけのQ太郎 おばけのQたろう Obake no Q-taro and ゲゲゲの鬼太郎 げげげのきたろう Gegege no Kitaro
The Tale of the Split Mouth Woman (口裂け女 くちさけおんな Kuchisake Onna)
In Japan, when people have colds they often wear a mask made of cotton gauze, so that their coughing doesn't spread germs around. (I remember that my mother wouldn't let me wear a mask when I had a cold, since she didn't believe they stopped the spread of germs at all and just turned nasty and moist on our faces. So of course, I was envious of my classmates who came to school wearing masks.)
In the 1970s, when I was in elementary school, a rumor spread throughout Japan of a beautiful woman, who was wearing a mask on her face. She would approach small children like me, and ask, "Am I beautiful?" The child would answer yes. She would then take off her mask, revealing a mouth that was horribly split from ear to ear, and ask again, "Am I still beautiful?" If you answered no, she would take out a sharp blade (either a kitchen knife or a surgical knife) and either slash you to death, or split your mouth so that it looked like hers...
This was really a variation of a bogeyman story, but it really spread like wildfire all around the country. There were various reports on the news with 'real' sightings. I lived in a suburb of Tokyo called Hachioji, and our school was about a 30 minute walk away. In the morning all the neighborhood kids would walk together to school in small, organized groups, but we all walked back home alone or in twos and threes. There was a long stretch of road that had no houses, just empty fields filled with tall ススキ susuki, a type of native grass plant with broomlike heads. My friends and I used to scare each other silly by coming up with more and more exaggerated tales of 口裂け女 sightings.
According to the Japan Wikipedia page about 口裂け女, this urban legend may have had its origins in the 18th century, and it had a revival of sorts in the 1990. It even spread to South Korea in 2004, and inspired a movie more than once. I do know that a whole generation of Japanese kids in the '70s and '80s, incuding me, were scared silly of the 口裂け女, for at least a brief period in their lives.
怖い！ こわい！ kowai! (scary / scared!)
The ghost season in Japan
Halloween is not really celebrated in Japan, since the holiday is really a Christian one with European pagan roots. The high season for ghosts in Japan is the summer. One reason is because of お盆 おぼん obon, a period in early August when people traditionally went back to their home towns to pray for the spirits of their ancestors. (Nowadays a lot of people just take the opportunity to go on a short vacation.)
There's a more practical reason for telling scary ghost stories in the summer though: when you're frightened, you can break out into a cold sweat (冷や汗 ひやあせ）, which can cool you down!
Have a happy and safe Halloween!