Namecoin is probably the largest, and provides .bit. IPFS has IPNS, but that is just subdirectories of a user hash, there is no pretty naming there.
There is also tech like what is behind .onion, where you can generate names until you get one you like, where you can devote more resources to getting prettier names at the cost of electricity and hardware to do so.
"Unlike DNS, GNS does not rely on central root zones or authorities. Instead any user administers his own root and can can create arbitrary name value mappings. Furthermore users can delegate resolution to other users' zones just like DNS NS records do. Zones are uniquely identified via public keys and resource records are signed using the corresponding public key. Delegation to another user's zone is done using special PKEY records and petnames. A petname is a name that can be freely chosen by the user. This results in non-unique name-value mappings as www.bob.gnu to one user might be www.friend.gnu for someone else."
Yes, this is an application where the blockchain wouldn't necessarily be stupid.
I don't see it as necessary, to be honest, and given the frequency with which people lose access to their wallets/have them stolen, I'm not entirely sure the bulk of domain owners would want bearer instruments to be the sole way to manage (or lose) their domain.