What`s the situation with private health insurance in Thailand? Is the Public Health Service good enough to take care of the needs of the sick, or are there definite benefits in having private insurance? How expensive is private insurance for those wishing to take it up?

what public health service? the 30 baht cure all diseases program?

There is no free health care-that I know of
so insurance is necessary

What about those people who are so poor that they can`t afford health insurance?

Well the Thaksin Regime introduced the 30 THB system, which covers general heath care for the poor.