Here are some free typing tutors to help you increase your overall typing speed using the virtual keyboard of your iPhone or iPod. You can also test your current touch-screen typing speed and learn about new tips to improve it.
TypingWeb – This is online typing tutor for iPhone with different modes for beginners or people who already know touch typing on iPhone but are looking to increase their overall wpm or typing speed.
iPhoneTypingTest – This website will help you test your typing speed on the iPhone – you can either take the test in landscape or portrait mode.
Kudit – This app for iPhone and iPod touch will calculate the words per minute of anything you type just as you would in an SMS or email.
David Pogue – Pogue shares some of his favorite tips for using the iPhone keyboard.
Typing Shortcuts – The very useful punctuation shortcut for typing in iPhone.
And this video demonstrates how fast some people type even with touch screen keyboards:
Related: Check out some touch typing tutors for the desktop.