drush

$ drush sql-dump --gzip --result-file=~/path-here/sql-dump.sql

I created my own shell script dump_db.sh to make less hustle.
Inside my dump_db.sh

#!/bin/bash

if [ -z "$1" ];
then
  echo "Please specify if its dev or prod" 
  exit 1
else
  dev="$1"
fi

if [ -z "$2" ];
then 
  echo "Please specify the database name"
  exit 1
else
  db="$2"
fi

echo "Exporting database"
drush sql-dump --gzip --result-file=~/backup/$(date +%Y%m%d-%H.%M)-"$dev"-"$db".sql

I would run this:

$ source dump_db.sh dev drupalista.net

$ gzip -d < db.sql.gz | drush sqlc

Create a php script with a header #!/usr/bin/env drush

my_php_script.php
#!/usr/bin/env drush
<?php 
echo drush_get_option('param');
exit();

Drush command to run the php script from cli

$ drush scr my_php_script.php --param="this is a test"

Drupal 6 and 7

$ drush cc

$ drush sql-dump > ~/my-sql-dump-file-name.sql

Drupal 8

$ drush cr

$ drush sql-dump > ~/my-sql-dump-file-name.sql

Download Database from the server

$ scp username@example.com:~/my-sql-dump-file-name.sql ~/projects

Import Database

$ drush sql-drop

$ drush sql-cli < ~/my-sql-dump-file-name.sql