If your using CSS in your extension pages (background, popup, infobar, etc) then you can use relative paths:
background-image:url("/sprites.png");
The above should work, everyone uses it. But, if your using it for content scripts and you can do the same for any css, you would need to use the predefined message like:
background-image:url('chrome-extension://__MSG_@@extension_id__/sprites.png');
If you want to programmatically set it, you can use the chrome.extension.getURL syntax as following:
var url = chrome.extension.getURL('sprites.png');
These are the ways that you can refer to a specific url/image.