Digital signature is one of the most important primitives in public key cryptography. It provides authenticity, integrity and non-repudiation to many kinds of applications. On signer privacy however, it is generally unclear or suspicious of whether a signature scheme itself can guarantee the anonymity of the signer. In this paper, we give some affirmative answers to it. We formally define the signer anonymity for digital signature and propose some schemes of this type. We show that a signer anonymous signature scheme can be very useful by proposing a new anonymous key exchange protocol which allows a client Alice to establish a session key with a server Bob securely while keeping her identity secret from eavesdroppers. In the protocol, the anonymity of Alice is already maintained when Alice sends her signature to Bob in clear, and no additional encapsulation or mechanism is needed for the signature. We also propose a method of using anonymous signature to solve the collusion problem between organizers and reviewers of an anonymous paper review system.