Just the other day, G was having problem with the ssl side of their servers for AdWords. One of our sites would hang on any page that had included their SSL script. Talk about a bummer for business! This went on for what appears to be at least 2 hours.
Before that, they were "overwhelmed" by the response they got with people signing up.
I'd be interested in hearing what experiences others have had (good and bad) with Google analytics.
Analytics and any other Google delivered services can seriously dent your page delivery speed when they are overwhelmed.