A tracker serves 2 purposes:
1) Hosting the .torrent file (which is basically just a list of checksums for each piece)
2) Initial matchmaking of peers, and keeping track of "who has what"
#1 isn't a huge problem, as the .torrent files are tiny and pretty simple to find. #2 is where most of the value of the tracker comes in, because it lets each peer in a swarm find out about the others, so they can connect directly. However, once peers have found each other they'll connect and communicate directly.
In the traditional torrent model, with a tracker, your client pings the tracker every 20 minutes or so for a list of new peers who have joined the swarm. From that list, you'll attempt to connect directly to new peers.
A DHT (distributed hash table) is a nice hack that is meant to take load off the central tracker. In essence, instead of always asking the tracker for a list of new peers or who has a specific piece, you can ask the peers you are already connected to. Its kind of like an office, where you ask questions of your coworkers before bothering your boss.
This is why you can download torrents even when the tracker is unreachable, or in this case, taken offline completely. This is also why you can download torrents from demonoid without a demonoid account - the account just gives you access to the demonoid tracker, which you don't necessarily need.
I'm a little hazy on how a swarm would start without a tracker, as it seems like a decently sized swarm is needed to get the ball rolling, so to speak. Perhaps someone else can jump in?
This is also why private trackers don't like DHT and discourage its use.
... upon looking, they still seem to publish .torrents for now, but the huge magnet icon on their home page pretty much tells it all :)
That doesn't mean the MPAA won't try, they've argued that file hashs are equivalent to the file before, and they may win in the US, however, I'm not sure that arguement would hold up in the EU due to the possibility of hash collisions, and the fact that you can't make the file from the hash.
Currently sites like torrentz.com give multiple trackers for torrents so that you can get the best set of peers/seeds for a torrent. These sites are going to become moot.
Also the legal issues associated with running TPB is going to literally go away for all future business. TPB can't be held responsible for holding an MD5 hash of a file, since they don't host trackers anymore they won't be responsible for even facilitating anything. Basically the record industries have to go after the customers yet again.
The only thing left is an IP masker mechanism which is super easy to use in torrents and torrents will become completely untraceable :P ok fine someone will find a way.