Joomla 1 and Joomla 1.5 Cyrillic issue fix:

In the file /libraries/joomla/database/database.php
Need to find the string $this->_table_prefix = $table_prefix; and put the following code after it:

@mysql_query("SET NAMES 'cp1251'", $this->_resource);
@mysql_query( "set session character_set_server=cp1251", $this->_resource );
@mysql_query( "set session character_set_database=cp1251", $this->_resource );
@mysql_query( "set session character_set_connection=cp1251", $this->_resource );
@mysql_query( "set session character_set_results=cp1251", $this->_resource );
@mysql_query( "set session character_set_client=cp1251", $this->_resource );

or, in the case with UTF-8:

@mysql_query("SET NAMES 'utf8'", $this->_resource);
@mysql_query( "set session character_set_server=utf8", $this->_resource );
@mysql_query( "set session character_set_database=utf8", $this->_resource );
@mysql_query( "set session character_set_connection=utf8", $this->_resource );
@mysql_query( "set session character_set_results=utf8", $this->_resource );
@mysql_query( "set session character_set_client=utf8", $this->_resource );