This post describes how you can backup your VMware ESXi home installation with free license using BazaarVCB if you do not have a vCenter Server available. Bazaarvcb is the fastest backup solution I have used on the free VMware hypervisor.
Download the latest version from the download page.

The backup script is run by crontab every night and looks like this

#!/bin/bash
bazaarvcbPath="/media/backup/bazaarvcb-0.9.7b-linux-i386/bazaarvcb"
backupsPath="/media/backup"
hostname="192.168.0.222"
username="root"
password="password"
rollOut="30"
vmNames="vm-guest1 vm-guest2 vm-guest3"

for VM in $vmNames; do
        `$bazaarvcbPath backup -H $hostname -u $username -p $password --roll-out $rollOut $VM $backupsPath/$VM`
done

The backups are full so make sure you have enough disk space available.

bazaarvcb options

$ bazaarvcb -h
usage: bazaarvcb [-h]  ...

optional arguments:
  -h, --help   show this help message and exit

valid commands:
    checkhash  check .hsh files integrity in one directory
    listvm     list registered VMs on the ESXi host
    queryvm    display VMs informations
    listbackup
               search for backups in local and remote directories
    querybackup
               display report file of one particular
    backup     backup a VM
    restore    restore a backup

Open TCP port 31031 in your firewall to ensure that you have a high transfer rate, otherwise the backup will be transferred over SSH protocol and will be capped in speed to about 7MB/s (on the free hypervisor).
Bazaarvcb cannot backup a VM with snapshot(s).

Warning!
I have not tested this on a host connected to a vCenter server and can not confirm that it will work or not.