I think you are thinking about Tanabata (七夕-たなばた). Those strips of paper where you write your wishes are called tanzaku (短冊 - たんざく).
You can read more about the festival and customs here:
Tanabata - Wikipedia, the free encyclopedia
Tanabata - Calendar 07 - Explore Japan - Kids Web Japan - Web Japan
70s と 80s年代 の 日本映画, CM, J-POP, TVドラマ と アクション刑事ドラマ 大好き!