If I buy a motherboard which "Supports Dual channel DDR2 800/667/533 Un-buffered Non-ECC memory" , do I have to use Un-buffered Non-ECC memory? Will a 2GB DDR2-800 240-Pin Module work?

You really should be more specific. The memory cannot be FB-DIMM, that is for server mobos.

Standard DDR2-800 is fine. They are both 240 Pin.

Right RAM - Non-EEC Unbuffered Desktop Memory.

Wrong RAM - EEC Fully Buffered Server Memory.