Out of the pretty small number of database systems I've used:
Postgres: Pretty standard choice, can't go wrong with it
MySQL/MariaDB: Also very safe choice, I feel like it's more feature rich than Postgres but I'm not sure
Oracle: It reeks of proprietary bloat and it's unnecessarily different than the previous two in some things, but you can get some official enteprise support if you're a company
Influx: It solves a specific problem (time series) but it's very cool, modern and with api support for many languages
Unpopular opinion probably, but Firebird has been really good to us for a couple of decades.
We have thousands of users running it to provide offline data and it's been extremely reliable and trouble-free. Good support for features like stored procedures, triggers, etc. without requiring much in the way of maintenance.
My biggest complaints are that the database file size tends to bloat up with lots of transactions, and it needs a better bulk-load feature (it has an 'external table' feature that works well and that we use heavily, but it's kind of a pain). And prior to v4 it didn't have a good replication system. No idea how good the replication in v4 is.
In our case, history mostly. The application we are using with it was originally developed (not by me) in the late 1980s in Borland Pascal and, I think, dBase. At some point in the early 1990s the original developers decided that dBase wasn't good enough and because Borland owned Interbase at that time and supported it with their coding tools, they decided to move to Interbase (later when Firebird was forked from Interbase they switched over to Firebird to avoid potentially needing to pay licensing fees on the numerous client computers).
The application, hugely expanded compared to what it was in the early days, has a great deal of Firebird-related code in it now, so moving off of it would be expensive and not really provide any return on the investment.