This website called TypeRacer is one I've used to significantly increase my typing speed. It basically tracks your typing speed in a game format but requires you to type perfectly to advance.
Rather, not my speed, but my accuracy. Once you get around 80-100wpm you start needing to be precise and perfect, the first time, to avoid all mistakes.
It's hard to practice this since we generally start using the backspace or other mechanisms by reflex, but having a place to enforce proper and first-time perfect typing will really make a difference.
A small amount of time on there will make you realize the importance of having a rhythm for your typing. This is contrasted to "bursts" where you are more prone to making mistakes. Focusing on each keystroke taking the same amount of time is a great way to do this. Like I said though, it's much easier with a site like TypeRacer (there are of course others, but this is the one I've used to increase my speed and accuracy).