The Google Pinyin Input is an input method (IME) optimized for typing Chinese on Android.

The app offers a variety of methods for fast and easy input of Chinese characters.
Key features:
– QWERTY Pinyin keyboard with gesture typing and intelligent correction
– 9 key Pinyin keyboard with gesture typing
– Stroke keyboard
– Full screen and half screen handwriting keyboard
– Latin keyboard
– Fuzzy pinyin
– Double pinyin
– Optimized UI for different screen sizes
– Voice input
– Themes

The app supports both simplified and traditional Chinese characters, as well as punctuation, emoticons, Latin characters and digits. Voice input is network-based in order to provide highly accurate matches.

Note: To be used on your Android device, the input method must be enabled in “Settings” → “Language & Input”.

For typing Cantonese, you could download the Google Cantonese Input:
play.google.com/store/apps/details?id=com.google.android.apps.inputmethod.cantonese

For typing traditional Chinese by Zhuyin or Cangjie, you could download the Google Zhuyin Input:
play.google.com/store/apps/details?id=com.google.android.apps.inputmethod.zhuyin