It's not possible to integrate into the actual "windows update" functionality of windows, however it is possible to use the same underlying technology for your update system if you would like to.
It's called Background Intelligent Transfer Service (or BITS), and comes with an API that you can use to let your application take advantage of it for your own updates. You would still have to totally manage the update process on your own though, BITS just takes care of the throttled background downloading of the update. There's also a
BitsAdmin tool that can be used to manage BITS streams.
Unless you are writing a pretty big app, you should think seriously before you try and use BITS, it's not a simple 'click and go' setup procedure, you'll have to manage the majority of the update process in your own code.
On the other hand, ClickOnce (as rjh has already mentioned) is fairly easy, you simply define some basic parameters like version and update URL, and the ClickOnce engine will automatically handle checking, downloading and installing your updates, all you have to do is publish them to the server. There are some restrictions to ClickOnce, but for a large number of apps, ClickOnce can work very well. For a standard ClickOnce deployment there is no code to write, it's all handled through the visual studio interface.