Kaki-gōri has a long history. In an essay "Makura no Sōshi[枕草子（まくらのそうし）](The Pillow Book)" by a female writer, Sei Shōnagon[清少納言] in the Heian Period(794-1185), Kaki-gōri(shaved ice with ivy syrup in metal bowl) was written as one of something elegant. But at that time, ice was cut in winter and was preserved in ice houses until summer and in the Edo Period(1603-1868), ice was presented to Shōgun[将軍（しょうぐん）](Shōgun was the most powerful position at that time.) in summer. So, ice was very precious, you know.
Kaki-gōri it became popular among common people in the Meiji Period(1868-1912) and in 1869, the first Kaki-gōri shop opened in Yokohama[横浜（よこはま）].
There are various syrups put on shaved ice. The most common syrups are strawberry, lemon, melon, Blue Hawaii(a blue-colored syrup flavored with fruit aroma) flavors. These flavored Kaki-gōri are standard in stalls of summer festival.
As for other Kaki-gōri, Mizore[みぞれ] or Sui[水（すい）] is a Kaki-gōri with non-flavored syrup. And Uji-kintoki[宇治金時（うじきんとき）] is a Kaki-gōri with Matcha[抹茶（まっちゃ）](green tea) syrup & sweetened Azuki[小豆（あずき）](red beans) or Anko[あんこ](sweetened red bean paste). That has elegant & light taste. Therefore, that is popular with adult.
There are also local Kaki-gōri. Shirokuma[白（しろ）くま] in Kagoshima[鹿児島（かごしま）] is a Kaki-gōri with condensed milk, fruits & Azuki. Shirokuma means white bear(polar bear) and that is because toppings on ice expresses polar bear face.
Zenzai[ぜんざい] in Okinawa[沖縄（おきなわ）] is a Kaki-gōri with boiled Kintoki-mame[金時豆（きんときまめ）](red kidney beans) with brown sugar. Zenzai refers to a sweets that is a sweetened Azuki except Okinawa.
And Shaved ice that was spread by Japanese American is popular in Hawaii.