Does anyone know what the resolution should be, if you're using a picture as your background, I've tried to use some of my desktop wallpapers (which is 1024*768) as the background, but then it looks all crappy because the messenger resize it, to fit in the window...
Is there a resolution that will fit perfectly without being resized?

You mean window as in: Conversation Window background, or the Window with your Display Picture?

The size of the conversation window varies from user to user (and computer to computer), so you will just need to make the correct stretches to it. You could find the approx. size by taking a print screen of your conversation window, and finding the w and the d of your window, which then you can use an editing program to crop + resize the picture at your discretion.

Your Display Picture has a fixed sized of 96 x 96. Therefore, you could simply use an editing program and resize + crop the picture at your discretion.

I'm talking about the conversation window...
What if my screen is 1024*768 and I've maximized the window then?

Then it should be about 900&758.

(I'm just estimating )