Chinese Chinese Lite (free) You are shown a Chinese character (traditional) and you trace it in the right order. A good intro to writing Chinese. This free version has Lesson 0, which is a tutorial on the basic elements of characters, and Lesson 1 with 32 words. You have to draw each character correctly to get to the next one. When you get more advanced, you can click to get rid of the grid and try to write the app without tracing it. One thing this app lacks is audio pronunciation of the characters.

Chinese Chinese ($1.99) This full version contains seven lessons with 32 words each, including more complicated characters (traditional).

Chinese Writer (free) This app uses an "invisible ink" kind of method - you draw the character on a blank screen and if you draw it correctly, it appears. It's a little buggy and you need to be a member of PopUpChinese.com to get full functionality.

iWriteChinese (.99) Really nice intro tutorial on basic strokes and stroke order rules. Step by step instructions on how to draw characters, with ability to practice and turn on or off the character in the practice box to see if you've drawn it correctly. App includes a simple quiz of character meaning, recognition, and pronunciation (but strangely, not writing). This app has no audio pronunciation of characters - which would help.