If you want to add more detailed tracking data, then you can use Custom Variables. If you want to add other traffic streams that GA is not capable of tracking (e.g. users with JS disabled), then that's more tricky.
One way you could achieve this is by creating your own reports or custom dashboard using Google Analytics' Data Export API. Just take your raw GA data, add your own server-side analytics data, and then use something like JavaScript InfoVis Toolkit, Google Charts, or jQuery Visualize to display the combined data.
Check out some of the other questions for self-hosted log-file-based analytics solutions which don't require JavaScript.