Ubuntu users:

$sudo apt-get install keychain

After its install, you set it up by entering the keychain command followed by your private key (not the public key).

$ keychain ~/.ssh/id_rsa
KeyChain 2.6.6; http://www.gentoo.org/proj/en/keychain/ Copyright 2002-2004
Gentoo Foundation; Distributed under the GPL</pre>
* Initializing /home/timmy/.keychain/hostname-sh file...
* Initializing /home/timmy/.keychain/hostname-csh file...
* Initializing /home/timmy/.keychain/hostname-fish file...
* Starting ssh-agent
* Adding 1 ssh key(s)...
Enter passphrase for /home/timmy/.ssh/id_rsa:
Identity added: /home/timmy/.ssh/id_rsa (/home/timmy/.ssh/id_rsa)

Keychain then creates three files which correspond to various shell environments. As I am using bash, the file I will be referencing will be /home/timmy/.keychain/hostname-sh.

$ source ~/.keychain/hostname-sh

To make sure everything is fine run the following to make sure the the environment is in fact set up:

$ env | grep SSH_A
SSH_AGENT_PID=9607
SSH_AUTH_SOCK=/tmp/ssh-bMoLeb9606/agent.9606

Of course you will want this to happen automatically on login so add the following to your ~/.bashrc

keychain ~/.ssh/id_rsa
source ~/.keychain/hostname-sh

The last step is to add the following line to your backup script (including the .)

. /home/timmy/.keychain/hostname-sh

Backup Scripts
Ill only mention the two methods that i use.
1. scp: To copy files from one location to another
2. rsync: To sync a remote location to local location

SCP

. /home/timmy/.keychain/hostname-sh
scp -r /home/timmy/Server_Backups/web/* root@192.168.0.1:/var/backup/web

Rsync

. /home/timmy/.keychain/hostname-sh
rsync -rzvhlc --delete -e "ssh -p 22 -i /home/timmy/.ssh/id_rsa -o 'BatchMode yes'"
root@hostname:/var/www/vhosts/vhostname/httpd/ home/timmy/Server_Backups/web/

After that you should not get the error:

Permission denied, please try again.
Received disconnect from 192.168.0.10: 2: Too many authentication failures for root
lost connection