The Adventures Of Buckaroo Banzai Across The Eighth Dimension

Adventurer/surgeon/rock musician Buckaroo Banzai and his band of men, the Hong Kong Cavaliers, take on evil alien invaders from the 8th dimension.

As promised, the trailer. Also if you go to the IMDB trailer page here, you get a huge selection of clips put together to try and explain whats going on - and it still fails.