They've let us do this now?
That link isn't the most descriptive thing. But, yes, its real easy.
Hit the Xbox button to bring up the mini guide. Then scroll over to the "Achievements" section. That will bring up all the games in your game history. When you go down the list, any game that has 0 points, it will give you the option to delete. It will remove it from your history both on the Xbox, as well as online. Basically its gone for good.
This works for full retail games, as well as XBLA games/trials. But, it only lets you do this with games with 0 points. So, if you are unlucky enough to have scored points in some stupid game, its stuck. A friend of mine has the misfortune of having 10 points in Yaris. And its going to haunt him forever now. HAHA!
The XBLA trials are what got me. A while back, I had my Xbox set to auto-download all new trials. Then, every couple weeks, I would go in, see what was new, and give them a whirl. Well, I soon realized that those trials were sticking in my history. I had like 30 of them. So, finally being able to take them out is nice.