Are there any types of distributed databases which allows untrusted peers, like Blockchain?
Distributed Hash Tables (DHT) are key value stores that work in a P2P manner, which is basically a database. There are implementations that don't rely on trust between peers. Obviously this can only be achieved by strong replication and consensus on the current value to a given key. So you face similar problems as with a blockchain.

The Wikipedia Article https://en.wikipedia.org/wiki/Distributed_hash_table will give you a good overview. Chord and Tapestry are probably the most famous DHT concepts.

If you want to look at applications instead The DHT approach is mostly used in peer-to-peer file hosting and file sharing.

There might also be other distributed databases or database-like concepts out there. This is just one I know.