I prefer Postgresql to MySQL even though I am using MySQL here as the backend of this web site. I am using MySQL because WordPress integrates better with it. More specifically, many optional WordPress plugins are written in a non-standard SQL dialect that PostgreSQL will not run. That tells you something about Postgresql. It is a stickler for the SQL standard and implements more of it than even many commercial products.
Besides adherence to the standards, Postgresql, performs well in practical applications. It scales well under increasing workloads. It has many backup facilities and redundancy features. It has carefully designed transaction processing logic that carefully maintains database integrity even during catastrophic failures. Postgresql is ready for primetime for commercial application when there is a lot of business risk.
The active Postgresql community has developed rich interfaces for many computer languages. Postgresql supports stored procedures. Postgresql provides facilities for high speed connection pooling for use with high volume web sites. Postgresql provides many programming tools as well as a fine administrative interface called pgAdmin-III.
Besides all this technological virtuosity, the Postgresql project keeps a very clean open source license and is not endangered by corporate entanglements.