update [table_name] set [field_name] = replace([field_name],'[string_to_find]','[string_to_replace]');
So if I wanted to change every occurance of "joomla" to "Joomla!" in the articles of this site I would use the query window of phpMyAdmin and type
UPDATE jos_content SET introtext=REPLACE(introtext,'joomla','Joomla!');