I have two servers running RHEL 5. Both have nearly identical configurations. I have set up RSA Publickey authetication on both, and one works but the other does not:

[my_user@client] $ ssh my_user@server1

--- server1 MOTD Banner ---

[my_user@server1] $

and on the other server:

[my_user@client] $ ssh my_user@server2
my_user@server2's password:

--- server2 MOTD Banner ---

[my_user@server2] $

server2's /etc/ssh/sshd_config file snippet:

RSAAuthentication yes
PubkeyAuthentication yes
AuthorizedKeysFile        .ssh/authorized_keys

When I run ssh -vvv I get the following snippet:

debug3: authmethod_lookup publickey
debug3: remaining preferred: keyboard-interactive,password
debug3: authmethod_is_enabled publickey
debug3: Next authentication method: publickey
debug1: Offering public key: /home/my_user/.ssh/id_rsa
debug3: send_pubkey_test
debug2: we sent a publickey packet, wait for reply
debug1: Authentication that can continue: publickey,gssapi-with-mic,passowrd
debug1: Offering public key: /home/my_user/.ssh/id_dsa
debug3: send_pubkey_test
debug2: we sent a publickey packet, wait for reply
debug1: Authentication that can continue: publickey,gssapi-with-mic,passowrd
debug3: authmethod_lookup password
debug3: remaining preferred: ,password
debug3: authmethod_is_enabled password
debug1: Next authentication method: password
my_user@server2's password: