For the most part, my IMs look exactly the way I speak. I have a friend that I sim with who I know has the ability to write correctly, but for some reason he likes to talk like....oh, sample!: 'ur goin 2 g 2 da chat 2day neway?' Or something horribly along those lines. And he's British! And reasonably intelligent! And I know he can write properly, because I've seen him do it! But he has to speak like that! ARGH!
As I was saying, in chatrooms and IMs I am, for the most part, typing the same way I do here, fixing my typoes immediately. But I do say things like 'I g2g' or 'ttyl' or even an occasional 'cya.' And of course I say stuff like 'lol' and use smilies. But I really try to stay correct.