Are there any furniture design competition or contest???  

Seek & U will find...
You could try Architect, Architectural Record, Metropolis....magazine back pages. They frequently have the classifieds, RFPs, manuf's. literature, design competions, etc. buried there. You don't need to purchase them just visit your local bookstore (if they have large selection of magz.). Good Luck!

designboom.com
Has a page devoted to furniture and other modern design competitions.

there's a bunch, but you...
there's a bunch, but you have to pay for all of them, which seems rather ridiculous to me...

furniture contest
can you tell me which one is the best furniture contest?
thank you