Well you can buy movies from Live as well, and have the movies stored on the Xbox. You can keep your music library on the Xbox and listen to it through the music player. These things can also be done via streaming and with USB thumb drives (now).
The original Xbox 360 had a 20G HDD and many of us used that for a couple of years with minimal issues. The USB thumb drive is capped at 16G so it is not that far off. What has changed over the last couple of years is that more and more content is going to be offered via download and they are trying to position the Xbox as a media center to offer many different things (movies, music with Zune, netflix, ESPN3, and the streaming capabilities with windows media extender), along with games.
Like others have mentioned, if you are not a hard core gamer, do not plan to (initially) download arcade games, add ons, etc, the Arcade is fine (save for the Halo Reach issue, which should get fixed). You can always add a HDD in the future. The cost difference would be ~$30. In the interm, you could always use thumb drives and save a little bit of money. If money is no object, get the Elite, if money is an issue, in the short term you would save a little getting the arcade, but likely in the long term you would end up spending more if you plan on adding HDD in the future. There is a reason why the HDD size has gone from 20G in 2005, to 250G in 2010. The only reason to offer an Arcade is to keep the cost below $200 which is an outstanding value, considering the PS2 was that price for years before it droped to $149 and less at the end.