Nic is right, they have to be turned on. You can do so through Administration->Issues->Issue Types, then Sub-Tasks tab.
This URL might take you right there: https://adicio.atlassian.net/secure/admin/subtasks/ManageSubTasks.jspa
I can't answer the first half of the question, but sub-tasks have been available in Jira since version 3...
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Sorry, I should really have mentioned that it needs to be switched on deliberately (although I don't know OnDemand, so I don't know exactly Atlassian have enabled off-the-shelf)
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Thanks Nic, your answer helped me understand that I didn't have Sub-Tasks enabled on my Jira OnDemand trial. I appreciate it.
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