Easy way to suppress output of fabric run?

It sounds like Managing output section is what you're looking for.

To hide the output from the console, try something like this:

from __future__ import with_statement
from fabric.api import hide, run, get

with hide('output'):
    run('mysqldump --no-data test | tee test.create_table')
    get('~/test.create_table', '~/test.create_table')

Belows is the sample results:

No hosts found. Please specify (single) host string for connection: 192.168.6.142
[192.168.6.142] run: mysqldump --no-data test | tee test.create_table
[192.168.6.142] download: /home/quanta/test.create_table <- /home/quanta/test.create_table

Try this if you want to hide everything from log and avoid fabric throwing exceptions when command fails:

from __future__ import with_statement
from fabric.api import env,run,hide,settings

env.host_string = 'username@servernameorip'
env.key_filename = '/path/to/key.pem'

def exec_remote_cmd(cmd):
    with hide('output','running','warnings'), settings(warn_only=True):
        return run(cmd)

After that, you can check commands result as shown in this example:

cmd_list = ['ls', 'lss']
for cmd in cmd_list:
    result = exec_remote_cmd(cmd)
    if result.succeeded:
        sys.stdout.write('\n* Command succeeded: '+cmd+'\n')
        sys.stdout.write(result+"\n")
    else:
        sys.stdout.write('\n* Command failed: '+cmd+'\n')
        sys.stdout.write(result+"\n")

This will be the console output of the program (observe that there aren't log messages from fabric):

* Command succeeded: ls
Desktop    espaiorgcats.sql  Pictures   Public     Videos
Documents  examples.desktop  projectes  scripts
Downloads  Music         prueba Templates

* Command failed: lss
/bin/bash: lss: command not found