So usually I develop with the 960 grid. But currently I have a design that could use a bit more space than 960. On the average screen 1050 wouldn't be a problem I guess, but I want this website to be optimized for mobile devices (iPhone, Ipad screens) too.
So what is the widest width I should consider?
You should consider media queries, which will allow you to present different widths for different browsers and screen sizes.
You should consider a fluid width, rather than a fixed width.
I think Tony's answer is spot-on as always. You really need to consider your users and adjust the width to what they are using. Personally, I find myself going back to a 960px width time and time again. It has worked great for me and most of my users that aren't accessing the site via mobile devices or smaller screens.