The only system I can see has to do with polling multiple hosts, taking the most popular response for a domain and routing that way, but then it is still something that can be overcome with enough machines on the network.
The Bitcoin approach that I've mentioned looks basically like the following:
Basically, you use Bitcoin's block chain described here: http://www.bitcoin.org/wiki/doku.php?id=block_chain However, instead of using the chain for monetary transactions, you store new domain registrations in each individual block.
Now you just need a mechanism to fend off the domain squatters. Again, we can use an approach similar to Bitcoin (and to Hashcash): If you want to store your registration in a block you need to "pay" for this with some CPU power. So if you want to register a given domain you need to calculate SHA-256(domainname + data), where data is chosen in a way that the first X bits of the resulting hash are zero. So basically you need to use a brute-force mechanism to find appropriate data. If it, e.g., takes on average 1 week to find this data, this is acceptable for an individual who wants to register a domain, but (hopefully) too expensive for a squatter.
However one problem with this approach is that there's no incentive for someone to participate in the block generation. In bitcoin participation gives you Bitcoins which have a real monetary value. But I think creating some incentive shouldn't be too hard. E.g., it should be possible to couple the block chain to Bitcoin, so that generating blocks for the secure domain system also gives you Bitcoins (as a side effect).
Using OpenAuth / OpenID / Facebook login etc. would mitigate the password problem.