While Microsoft might not appreciate it too much, Reddit users have found a way to block the ads (which many find to be obnoxious) being served up post-Xbox Live dashboard update. People tired of seeing that Chuck Norris World of Warcraft ad (for the record I love that ad!) in the Xbox Live dashboard got together on Reddit and created two work-arounds. One involves blocking the ad server in your router - assuming that it supports it. Another method is to reroute your traffic with the free OpenDNS service.
Both methods require some small measure of advanced knowledge about changing settings on your Xbox 360 and your router. You can read up on both methods by visiting this Reddit post.
Use this knowledge at your own risk - we do not advocate either way - but we will say that consumers should have the right to do what they will with the hardware they paid for.