Wait, hold your horses! You may not notice much improvement in your loading times after all, at least when it comes to anything recent. Turns out that newer 360 games have already had their file structures optimized on-disc to minimize load times to such an extent that running from the hard drive won't help much. Older games that didn't get this treatment will still see noticeable enhancement, though. Gizmodo has the scoop, straight from Microsoft Germany.
There are prominent examples, for instance: Project Gotham Racing 3, one of the first games for the Xbox 360. There the load times have been very long; those are going to get reduced immensely. Recent games are already optimized; there the gain is relatively small.
Bummmmerrrrrrr, dude. If that famous precision German engineering can't solve the problem, we're all screwed. I was waiting for this feature to jump back into GTA IV just so it would run more smoothly and get missions loaded faster, but it seems that won't be the case. Guess that's a dumb reason to not be playing one of the best games of the year, anyway; it's not like it runs poorly as is.
On the plus side, at least you won't have to listen to that jet engine of a DVD drive whirring away while you're playing from hard drive.