As a "full stack" developer our area of expertise is in the small to medium size business and on Unix/Linux based hardware. That means that for the most part we work on Macintosh and Linux based systems where we do the installation and take responsibility for management and administration. All database systems seem to share a majority of their features with the others making them somewhate easy to work with. For most of these listed below you can make an entire career out of just one of them.
1. Oracle - has been around for almost 35 years. It is complex but solid. A true enterprise solution.
2. Microsoft SQL Server - another solid product from Microsoft. We've worked with this database system in many different solutions.
3. DB2 - this product from IBM runs on Linux among other operating systems. This products competes with Oracle in the data center.
4. Sysbase - another database system that's been around for multiple decades. Like about 25 years. It's not a popular as it once was but appears to be making a comeback. Particularly with mobile device data solutions.