DataGrip/ IntelliJ IDEA Ultimate Edition
If you are already a user of Jetbrains tools, you may try DataGrip (or the database plugin, when you are an IntelliJ IDEA Ultimate edition user). This is quite new, but suitable for most use cases.
https://www.jetbrains.com/datagrip/
DBVisualizer
DBVisualizer is a very good solution for connecting to "any" DBMS with lots of features. There is a free version avaible, but the pro version is really worth the money:
http://www.dbvis.com/
HeidiSQL
A free and very good client for MySQL, PostgreSQL and SQL Server. It really evolved the last years.
http://www.heidisql.com
Squirrel SQL
Another quite good tool is Squirrel SQL. It's not the most intuitiv and beautiful tool, but has many useful features too:
http://squirrel-sql.sourceforge.net/
DBeaver
Another open source tool with a free community edition.
This is something for Eclipse users, as it is build upon Eclipse and can be installed as Eclipse plugin as well.
https://dbeaver.io
MySQL Workbench
This is not for PostgreSQL, but my answer is quite generic, so I wanted to add this as well.
MySQL Workbench is the officiel tool from Oracle for connecting to MySQL. It is really good for working with MySQL.
https://www.mysql.de/products/workbench/
Others:
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