“PostgreSQL: The World’s Most Advanced Open Source Relational Database”.
Relational databases are what comes to mind when just a database is mentioned without considering non-relational or other types. So we can say PostgreSQL is the technology that comes to mind when anyone needs a server-client application to store data. Of course there are lots of great alternatives like MySQL, MariaDB or SQL Server and of course they have strengths of their own. But considering the wide range of possible use cases, PostgreSQL is still the safest bet.
We generally prefer PostgreSQL when requirements fit and use it in as many solutions as the next guy, so specifics are not that important. Broadly speaking we see that PostgreSQL works great for applications requiring low-latency read-write access or multi-table transactions or even unstructured data. We also use it as a data warehouse with retention policies supporting OLAP style cases. Operationally speaking, synchronous replication in recent releases coupled with a manager is a pretty solid clustering solution.
As is the case with most technologies - even more so in more popular tools like PostgreSQL, it’s not what a tool can or cannot do, it’s how you use it. Simply put, questions like “is this the right way to access my data” or “is this the right hardware for my requirements” must be answered before jumping to the obvious conclusion of “it doesn’t work!”.