On their 2006 1099-MISC forms, my retired parents were paid in Box 7 (Non-employee compensation) as "independent contractors". This is the first time they have received these. In addition, they had worked whenever healthcare service agencies needed them, and consequently they have never "owned" or registered a "business". Is it correct that the IRS usually considers this to be self-employed business income? - Which would mean that they would be required to report on Schedule C.
Do they have to have registered a "business" or do they now have to obtain a Business Tax ID Number (EIN)? Lastly, they worked on-and-off: should they have paid during the year and does this mean they will be penalized? What can they do?

Yes, it IS considered self-employment income and, yes, they must file Schedules C and SE.

They do NOT need to get an EIN.

They will probably owe taxes for 2006, but there will be no penalties for under-withholding since this is their first year. They may want to begin making quarterly estimated payments using Form 1040-ES.

My daughter was in a simialr circumstance. She worked as a paid campaign worker last year and received a 1099-Misc for the amount she was paid. She had to use a Schedule C to report that income.

The advantage is that your parents can deduct any expenses that had in doing this work.

Agrred. Schedule C allows for a LOT of expense deductions.