Google in the past only sent you alerts via Webmaster Tools when your site was hacked, had malware on it, needed a software upgrade or had serious spam issues.

Now, Google will send you alerts via Webmaster Tools (and email it to you if you set it up to forward to email) when you get crawl errors.

Google will send you alerts for both site wide and page specific issues.

Site wide alerts include:

Your DNS server is down or misconfigured.
Your web server itself is firewalled off.
Your web server is refusing connections from Googlebot.
Your web server is overloaded, or down.
Your site’s robots.txt is inaccessible.

Page specific alerts that are less critical include:

Server error
Soft 404
Access denied
Not found
Not followed

Do you have alerts forwarding to your email? If not, set it up!

Forum discussion at Google+.