Our number is closer to 1,700 now, but yes this means 1,700 distinct applications. Each application has many instances, some have thousands of instances.
Uber runs a lot of databases in production. We stopped using Postgres a while ago for new applications that talk SQL, and this article explains some of the reasoning.
We still have many applications that talk directly to MySQL, and we still have our original API monolith that talks directly to Postgres.
All new applications are being built using distributed databases like our in-house Schemaless system which happens to be backed by MySQL, and we also have Riak and Cassandra in production.