How do I ssh without a password (setting up ssh keys doesn't work)?

Set the permissions on ~/.ssh (0700) and its contents (0600) on both the client and server appropriately.

ssh is paranoid about ownership of the authorized_keys file. If it is possible for someone other than root to change the file, then it won't use it. It checks the whole directory tree, so if it is possible for someone to do something like replacing your home directory or your .ssh directory it will not use it. Check the permissions from authorized_keys all the way down to /. None of these should be group or world-writable without the sticky bit set. (Permissions on my /home directory is drwxrwxr-t. Ownership must be root or the user. Permissions on the authorized_keys file should not allow access by group or world.

Testing with ssh -v instead of ssh should help. Using ssh-copy-id to copy the key to the remote system is a good idea.