It looks like all the Xbox Live problems were due to the rush of new subscribers combined with everyone using the service during the holidays according to this post
at Major Nelson. It's a bit disappointing that once again Microsoft failed to plan adequately for the rush of new users but it is what it is. Microsoft will be offering all Xbox Live members access to a free game to be named later.
The statement from Xbox Live GM Marc Whitten doesn't specify if this is exclusive to Gold (i.e. paying) members or not but I'm hoping that's the case.
Update (Chuck) - Major has said via Twitter
that the game will be available for BOTH Gold and Silver Members. I'm not sure how you reward you paying and non-paying members for a service outage with the same thing (especially since match making was hit hard) but we'll see how this all shakes out.
What do you all think? Should Microsoft offer one thing to everyone or one thing for Silver members and one thing for Gold members. Leave your thoughts in the comments.