With the free ESXi edition your options for VM based backups are limited. You may want to take a look at e.g. ghettoVCB (http://communities.vmware.com/docs/DOC-8760) or Trilead's VM Explorer (http://www.trilead.com/Documents/4.1/VMExplorer_Factsheet_en.pdf) to see whether these meet your needs.
If you are looking for more advanced features you may consider to purchase a vSphere "Essentials Kit" which unlocks the API and allows the use of a lot of backup applications (e.g. Veeam Essentials, ...)
Other than VM based backup applications, you cn still use OS agent based applications as you would do in a physical environment.
André