Error with drush clear-cache: Base table or view not found
Here is how to reset your cache_rules table, using a stable Drupal installation.

Get cache_rules structure from clean database

You can get SQL text to drop/add the cache_rules table via the following steps:


Log in to phpMyAdmin on a functional Drupal site. 
Click on the columns section under the cache_rules table
Click the Export button
Click 'Custom' to show all options
Under 'Output' click 'view output as text'
Under 'Format-specific options' choose 'structure'
Under 'Object creation options' check 'Add DROP TABLE / TRIGGER statement'
Copy the text displayed, or see below (sorry for the formatting)


Here is the SQL code to drop and add the table (thanks duckx!).

DROP TABLE cache_rules ;
CREATE TABLE IF NOT EXISTS `cache_rules` (
  `cid` varchar(255) NOT NULL DEFAULT '' COMMENT 'Primary Key: Unique cache ID.',
  `data` longblob COMMENT 'A collection of data to cache.',
  `expire` int(11) NOT NULL DEFAULT '0' COMMENT 'A Unix timestamp indicating when the cache entry should expire, or 0 for never.',
  `created` int(11) NOT NULL DEFAULT '0' COMMENT 'A Unix timestamp indicating when the cache entry was created.',
  `serialized` smallint(6) NOT NULL DEFAULT '0' COMMENT 'A flag to indicate whether content is serialized (1) or not (0).',
  PRIMARY KEY (`cid`),
  KEY `expire` (`expire`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8 COMMENT='Cache table for the rules engine to store configured items.';


Drop/add the cache_rules table

Now navigate to the other database, using phpMyAdmin. 


Make a full backup of the database
After the backup has been saved, click the SQL tab
Paste the text into the text box (removing any existing text)
Click 'Go'