Yes there are many tongue twisters in Japanese.
Here are some "classics".
東京特許許可局
とうきょうとっきょきょかきょく Tokyo tokkyo kyokakyoku
*Tokyo Patent Authorization Office (kyokakyoku... part is a bit difficult.)
隣の客はよく柿食う客だ
となりのきゃくはよくかきくうきゃくだ tonarino kyaku wa yoku kakikuu kyaku da
*Guest at neighbour is a guest who eats persimmon a lot.
竹薮に竹立て掛けたのは竹立て掛けたかったからだ
たけやぶにたけたてかけたのはたけたてかけたかったからだ
takeyabu ni take tatekaketanowa take tatekaketakattakarada
*I put a bamboo against the bamboo bush because I wanted to put a bamboo against the bamboo bush.
生麦生米生卵
なまむぎなまごめなまたまご namamugi namagome namatamago
*Raw wheat, raw rice, raw egg
赤巻紙青巻紙黄巻紙
あかまきがみあおまきがみきまきがみ akamakigami aomakigami kimakigami
*Red rolled paper, blue rolled paper, yellow rolled paper
(kimakigami part is a bit tricky!)
Even typing them out is difficult...
haha
Hope you'll enjoy them!