How well does DRBD (Distributed Replicated Block Device) work with either MySQL or PostgreSQL?

DRBD is not for every kind of MySQL setup. If all your tables are MyISAM and a failover occurs, chances are there will be marked as crash when the old DRBD Secondary becomes the new DRBD Primary. Any MyISAM tables that were just reads only would be fine in most cases but may still need a REPAIR TABLE command run against it to clean up it header info, If all your tables are InnoDB and a failover occurs, you will have to be patient while mysql on the new DRBD Primary performs InnoDB Crash Recovery to bring all tables back to a consistent state. How long you wait depends on how many tables were open, how many transactions have to be rolled back or committed. Other than waiting for Crash Recovery, DRBD is reliable for an all InnoDB Setups.

DRBD is great for an active/passive setup regardless of what you are running on top of it.  It was a common approach with PostgreSQL prior to replication having first class status in the project and still helpful for file servers and other things that don't support an active/active configuration. If you can have a replication slave instead there is no reason to use DRBD.  I greatly prefer active/active failover setup as they are easier to verify and feel good about.

DRBD is the right tools to just fool yourself. It gives you a false feeling of security in most case. The problem lies in the degraded mode. An exemple to understand the problem. We have two servers with DRBD in C protocol (full sync to disk): A is the master, B is the slave. Data are accessed only on A. B is the backup. An incident happens on the server A and it lost his connectivity to B, but everything else works. Data is no more replicated on B.  AND A continues to serve new transactions in DEGRADED mode. Next, the incident gets really bad and the A server dies. We can not recover the server A, and we can not switch to B because there are few transactions in A that was not sync with B. Conclusion: If you allow a degraded mode, you fool yourself. If your replication solution (other than DRBD) does not have a degraded mode, the safety of your data is better, but the availability of the cluster is worst. Because, as soon as one of the two servers has a problem, the service shuts down. In PostgreSQL, if you use synchronous replication, there is not degraded mode. The data are safe, but the availability is down. You need to use a third server to have a better availability.