When you talk of limited broadband, you mean you are limited in bandwidth usage per month. Everything that needs an internet connection uses bandwidth, in varying amounts. AIM, Limewire, browsing websites, etc.. Streaming or downloading video uses more than most anything else, practically. Playing a multiplayer video game over Xbox Live uses a pretty hefty amount of bandwidth.

If you are limited to a number of GBs of bandwidth per month with your internet service, then you should probably forget about Xbox Live. It's going to eat that bandwidth right up.