Examples:

• proprietary: Microsoft Access, Filemaker (Mac);
• open source: MySQL, SQLite;
• XML databases: eXist, baseX

Advantages:

• databases (or 'database management systems') can store, retrieve and manipulate much larger and more complex datasets than spreadsheets
• most database systems are 'relational': this means that multiple tables can be linked together using "key" fields.

Disadvantages:

• database software is not as easy to learn to use; open source databases in particular tend not to have friendly user interfaces; MySQL requires a server for installation
• you need to spend much more time planning and designing your database before you can get started. (But from the data management point of view this may not be a disadvantage at all!)
• databases are primarily storage rather than analytical tools; for most analysis and visualisations you will usually need additional software.