Touch typing has been the standard input method for computers (and typewriters) for a very long time now (since 1888 according to Wikipedia). Ever since we started shrinking the computer to fit in our hands, we've been looking at different ways to input text simply because touch typing is not very practical or efficient at that scale.
Not thinking outside the box
The easy answer is to simply put a full QWERTY keyboard on the phone/PDA and try to make the buttons as easy to hit as possible with minimal errors. Numerous phone makers have tried this and very few succeed. Most of the time, it's impossible to accurately hit the right key because the keys are not distinct enough. Blackberry's been known for providing great keyboards and my old Palm Treo 680 also sported a very usable keyboard. Sadly, very few phone makers get it right and what's right for someone might well be very wrong for someone else.
When a phone is not wide enough, phone makers have no choice but to use a standard numeric keypad (although inverted in comparison with a computer numeric pad). Needless to say, this method is far from optimal, requiring the user to type between up to 8 (or more?) times on a single key to get a single character. The T9 technology helped reduce the problem of such keypads, but it still requires a lot of keys to write a readable sentence.
Rethinking typing methods
Palm's Graffiti is one of the first experiments at improving the way we input text on a smartphone/PDA. It offered an alternative alphabet of symbols to be drawn inside a touch sensitive area of the screen. Each symbol looks like it's corresponding letter so that the user can quickly learn to write efficiently. The method has its limit because it still requires a lot of work from the user and requires the user to learn a new way to input text.
Swype: the current world leader in typing speed on a touch screen
Swype combined all of the previous technologies into a single one to produce the current fastest input method for touch screens. Indeed, Swype combines the proven efficiency of the QWERTY layout, the predictive text algorithms and the speed of simply swiping your finger around on the screen to make a very powerful input method. Furthermore, Swype's implementation allows it to learn how its user types and improves over time. As a user of this method, I must say that it truly is a worthy alternative to touch typing and even achieves similar typing speed (for average users) while only requiring one hand.
Back to basics with a twist
The biggest loss when transitioning from a physical keyboard to a touch keyboard, is the loss of the feel. Keys are all and there's no way to distinguish them or to be sure we hit the right one without looking. That's where BlindType comes in. Feeling that we hit the right key is nice, but what we really care about is that we wrote the right word. BlindType is similar to Swype in that it determines what word you probably wanted to write based on what you entered, the only difference is that with Swype you enter a trace while with BlindType you enter a series of taps.
What's wrong with QWERTY?
While others are out there trying to reinvent the way we input text by leveraging the differences that come with a touch screen, Microsoft comes out with a ridiculous attempt to keep the QWERTY keyboard alive. Fortunately, Microsoft's experiment is just that, an experiment: RearType is a prototype that puts two halves of a full QWERTY keyboard under a tablet PC so that each hand can reach the same keys as on a standard keyboard. I can't even imagine how anyone thought this would be a good idea, it's bulky and probably difficult to use.
What can we expect in the future?
With all those new ways of inputting text into our smartphones/PDA and tablet PCs like the iPad, we can get a taste of what's to come. The touch screen is becoming more and more prevalent and the software powering the touch keyboards are now correcting our mistakes. The standard physical keyboard is still the fastest input method on a computer, but we see the gap shrinking fast. Until I can write with my mind alone, Swype will be my method of choice.