前提：

1. /etc/ssh/sshd_config 配置正确；
2. 在远程服务器上添加了公钥；
3. 远程服务器ssh端口正确并且是默认的22端口；
4. 使用用户名与密码登陆正常；

问题：

1. 无法使用公钥登陆，每次都要求输入用户名与密码；
2. 普通用户可以公钥登陆，root不行，但sshd_config中是允许root登陆的且各种配置都正确；

登陆时提示如：
dengqingyong@bogon:~$ ssh egit-root
Permission denied (publickey,gssapi-keyex,gssapi-with-mic,password)

原因

问题1可能原因：文件及文件夹权限问题

权限要求如下：
~/.ssh/authorized_keys: 此文件要求权限为600
~/.ssh: 此文件夹要求权限为700 （我忽略了此权限，导致一台服务器始终无法用公钥登陆，设置后正常）
为了避免权限问题，建议尽量不要手动添加，采用命令添加，命令如下：

# 生成密钥（遇到提示可以一路回车，具体作用请查看帮助）
ssh-keygen -t rsa
# 上传公钥
ssh-copy-id -i ~/.ssh/id_rsa.pub user@remoteServerIP

问题2可能原因：selinux开启导致

selinux开启时，普通用户可以登陆，但root不允许登陆
解决方案：关闭selinux

#!/bin/bash
# 临时关闭selinux（0：关闭；1：开启）
setenforce 0
# 永久关闭selinux（disabled：关闭；enforcing：开启）
vi /etc/selinux/config  
SELINUX=disabled

测试

在正常的登陆语句后面加上-v即可查看登陆时与服务器交换的详情，-vv更详细
dengqingyong@bogon:~$ ssh egit-root -v
OpenSSH_6.9p1, LibreSSL 2.1.8
debug1: Reading configuration data /Users/dengqingyong/.ssh/config
debug1: /Users/dengqingyong/.ssh/config line 39: Applying options for egit-root
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 21: Applying options for *
debug1: Executing proxy command: exec ssh -q -W 192.168.1.62:22 gwe
debug1: permanently_drop_suid: 502
debug1: identity file /Users/dengqingyong/.ssh/id_rsa type 1
debug1: key_load_public: No such file or directory
debug1: identity file /Users/dengqingyong/.ssh/id_rsa-cert type -1
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_6.9
debug1: Remote protocol version 2.0, remote software version OpenSSH_5.3
debug1: match: OpenSSH_5.3 pat OpenSSH_5* compat 0x0c000000
debug1: Authenticating to 192.168.1.62:22 as ‘root’
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug1: kex: server->client aes128-ctr umac-64@openssh.com none
debug1: kex: client->server aes128-ctr umac-64@openssh.com none
debug1: SSH2_MSG_KEX_DH_GEX_REQUEST(1024<3072<8192) sent
debug1: got SSH2_MSG_KEX_DH_GEX_GROUP
debug1: SSH2_MSG_KEX_DH_GEX_INIT sent
debug1: got SSH2_MSG_KEX_DH_GEX_REPLY
debug1: Server host key: ssh-rsa SHA256:npT3KAq+nbSjgRVKutJre9aq8GcWPq1cnykDN8ImkCY
debug1: Host ‘192.168.1.62’ is known and matches the RSA host key.
debug1: Found key in /Users/dengqingyong/.ssh/known_hosts:80
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug1: SSH2_MSG_NEWKEYS received
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug1: Next authentication method: publickey
debug1: Offering RSA public key: /Users/dengqingyong/.ssh/id_rsa
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug1: Offering RSA public key:
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug1: No more authentication methods to try.
Permission denied (publickey,gssapi-keyex,gssapi-with-mic,password).
dengqingyong@bogon