(Written ages ago and never posted, but these things keep coming up)

1. Fault tolerance. Broadband connections that keep dropping out; moving from hotspot to hotspot with a mobile wireless device; unreliable electricity supplies; working offline; resuming; streaming; buffering; caching. BitTorrent does the best job yet of making a resumable P2P network that starts up where it left off next time you reconnect. DownThemAll makes resuming downloads in Firefox really easy. Amarok, on the other hand, does a poor job of fetching podcasts on an unstable connection. Lots of other web processes seem to just give up if they can't connect first time - this is especially important in AJAX applications, where you can't just hit 'reload'.
2. Collections. There are torrents of all the MAME ROMs (15GB); every Amiga Kickstart ROM, demo and game (4GB); every Nintendo DS ROM; discographies of artists; etc. Record labels are buying up back catalogue and concentrating on making them available for purchase, digitally. 'Director of the month' collects all the films by a director into one place. TV.com catalogues all the episodes of TV shows; discogs.com, Musicbrainz and last.fm do the same for music. I haven't seen anywhere that curates collections of digital/digitised art, yet. Lots of comics though.
3. Metered website hosting: stick a coin in the slot, the site runs until the money runs out. With metered hosting on EC2 and S3 this could work, discounting problems with freeloaders.