So I can find out if google is having any problems?

Google.com should never be down. So there's no need for a Status page for it, as Blogger does. [ http://status.blogger.com]
If you are talking about other Google problems, they are not publicized, only share among Googlers INTERNALLY.

And sometimes, even Google is down...
http://blogoscoped.com/archive/2005-11-22.html

I always ping google to check if my internet is down. Google == Internet. So if google is down, I'm checking my cables :P