Ubuntu – Postgresql table drop taking very long time

You can try the COPY command, but note that this sucks for incremental backups.

Another (possibly better depending) option may be a hot standby server that you shut down and take (filesystem-level) backups of periodically - This lets you use smarter tools which may take a binary diff of the DB table files and not have to suck down the whole thing every time you make a backup.
The other advantage is you have a well-knwon and well-supported recovery path this way :-)

This seems like locking problem: some large query locks too much, so other running queries cannot complete until lock is freed. Turn on slow query logging, add more monitoring. I strongly suggest using some monitoring system (zabbix, zenoss, etc) to be aware of your postgresql database status.

As a quick 'monitoring', take a look to pg_stat_activity and pg_locks views during the hang. Here is a good query that I'm often starting with:

SELECT
  datname, 
  NOW() - query_start AS duration, 
  procpid, 
  current_query 
FROM
  pg_stat_activity 
WHERE
    current_query <> '<IDLE>'
  AND
    NOW() - query_start > '1 second'
ORDER BY duration DESC;

It often gives enough information, but sometimes I have to run more in order to understand what's going on.

Please update your question with output of this (or similar) query.