After 25 years of persistence, and a better logo design, Postgres stands today as one of the most significant pillars of profound achievement in free software, alongside the likes of Linux and Firefox. PostgreSQL has taken a complex problem and solved it to such an effective degree that all of its competitors are essentially obsolete, perhaps with the exception of SQLite.
For a start, Postgres is simply an incredibly powerful, robust, and reliable piece of software, providing the best implementation of SQL.2 It provides a great deal of insight into its own behavior, and allows the experienced operator to fine-tune it to achieve optimal performance.
It supports a broad set of SQL features and data types, with which I have always been able to efficiently store and retrieve my data. SQL is usually the #1 bottleneck in web applications, and Postgres does an excellent job of providing you with the tools necessary to manage that bottleneck.