Though simplified Chinese characters are used in mainland China, traditional Chinese characters are still used in Taiwan, Hong Kong and Macau.
Kanji is derived from traditional Chinese characters, but has its own set of simplifications. They are not as extreme as simplified Chinese characters, and in fact looks very similar to traditional Chinese characters for the most part.
Incidentally, there are other writing systems which evolved from traditional Chinese characters just like Kanji did, such as Hanja (used with Korean, though losing popularity recently) and Chữ Nôm (used with Vietnamese until 1949)
Historically for China and Japan, complex writing systems did not fall out of use because people found them hard to use. They fell out of use because the governments decreed that it be replaced with a simpler version. So people in Japan don't have it as hard as people in Taiwan, Hong Kong or Macau when it comes to writing characters, but they don't have it as easy as mainland China. Unless the government adopts the Chinese writing system (unlikely), it's going to stay that way.
Now, would Kanji ever be replaced by Hiragana and Katakana? After all, Hangul is replacing Hanja in Korea. The answer is no. In Japan, there are so many homonyms that Kanji is necessary to decipher meaning.
This is a bit of a ramble but I tried to stick to comparing the complexity which rises from writing the characters themselves, as opposed to reading them or their cultural compatibility etc. Please read http://en.wikipedia.org/wiki/Kanji for a more thorough introduction. Hope this helps!