$query = mysql_query("SELECT * FROM kelimeler WHERE ( kelime_oyun = 1 AND kelime_onay = 1 AND kelime_id != '$id' ) ORDER BY RAND()");
Yerine

$query = mysql_query("SELECT * FROM kelimeler WHERE ( kelime_oyun = 1 AND kelime_onay = 1 AND kelime_id <> '$id' ) ORDER BY RAND()");
veya 

$query = mysql_query("SELECT * FROM kelimeler WHERE ( kelime_oyun = 1 AND kelime_onay = 1 AND NOT(kelime_id = '$id') ) ORDER BY RAND()");
de kullanılabilir. Kolay gelsin.