Connecting to an external database with pgAdmin III I'm trying to connect to an external database from pgAdmin III (which is installed on both machines).
The client complains:


  Access to database denied
  
  The server doesn't grant access to the database: the server reports

FATAL: no pg_hba.conf entry for host "192.168.108.161",
                                user "postgres",
                            database "postgres",
                                 SSL off 

  
  To access a database on a PostgreSQL server, you first have to grant primary access to the server for your client (Host Based Authentication).
  PostgreSQL will check the pg_hba.conf file if a pattern that matches your client address / username / database is present and enabled before any SQL GRANT access control lists are evaluated. 
  
  The initial settings in pg_hba.conf are quite restrictive, in order to avoid unwanted security holes caused by unreviewed but mandatory system settings.
  You'll probably want to add something like 

host all all 192.168.0.0/24 md5 

  
  This example grants MD5 encrypted password access to all databases to all users on the private network 192.168.0.0/24.
  You can use the pg_hba.conf editor that is built into pgAdmin III to edit the pg_hba.conf configuration file.
  
  After changing pg_hba.conf, you need to trigger a server configuration reload using pg_ctl or by stopping and restarting the server process. 


Where the server explicitly states that all connections from the internal network are accepted.

pg_hba.conf

# TYPE  DATABASE        USER            ADDRESS                 METHOD
# "local" is for Unix domain socket connections only
local   all             all                                     md5
host    all             all             127.0.0.1/32            md5
host    all             all             ::1/128                 md5
host    all             all             192.168.0.0/24          md5


I have already restarted the postmaster for the changes to take effect, and have gone so far as to restart the entire machine.
What else could be going wrong here?
This line:


 host    all             all             192.168.0.0/24          md5


will let through connections from IPs matching 192.168.0.X where X is any byte.

The IP address of your error message being 192.168.108.161, it does not match this pattern because 108 is not 0.

To enable addresses like 192.168.X.Y, you'd need a /16 instead of /24 meaning that the first 16 bits only are fixed.

Like this:


 host    all             all             192.168.0.0/16          md5


Don't forget to reload Postgresql. From the official docs, use pg_ctl reload. If that doesn't work, then there are other ways to do it listed in this question.