Can same private key generate multiple addresses? Is this possible using some clever bitcoin script? The intention is to get more privacy. I can give different addresses to different people still no one can guess how much I make in total. I can do this by generating several key pairs but I will have to save all the private keys somewhere. If I can come up with a way to generate multiple addresses, I will have to save guard only one private key.
One private key maps onto two addresses - one that uses an uncompressed public key, and one that uses a compressed public key.

What you might also be interested in is a deterministic wallet - a Bitcoin wallet holding multiple addresses generated from one private key / secret. This will let you secure multiple addresses and store only one key.