Going down the list, you have:
authorized_keys2 - this file contains public keys that are allowed to remotely login to this account (i.e. the accompanying private key is on a different machine)
known_hosts - this file keeps track of the servers you know about so ssh can let you know if it doesn't recognize the server you're contacting, or if the server key has changed for a server you used to know (which could mean someone is executing a man in the middle attack)
identity - your RSAv1 private key
identity.pub - your RSAv1 public key
id_rsa - your RSAv2 private key
id_rsa.pub - your RSAv2 public key
id_dsa - your DSAv2 private key
id_dsa.pub - your DSAv2 public key
What to do from here depends on whether that directory you just listed was on the server (where you'll be ssh-ing TO) or the client (where you'll be ssh-ing FROM).
Basically, you need to copy a public key (e.g. ~/.ssh/id_rsa.pub) from the client machine and paste it into the ~/.ssh/authorized_keys2 file on the server machine.
Then you should be able to ssh from the client to the server without a password.