As you are not a tax resident in India, the income you have earned can be moved to India tax free. However if you are investing the funds into say shares / fixed deposits etc, the income you earn on these funds is taxable in India.
The funds can be transferred directly into savings account. However its advisible to open an NRE/NRO account as its easier to track funds for tax purposes. i.e. these accounts by nature certify that the funds received into them are from foreign sources and can easily be explained to the tax authorities. However establishing the origin of funds in ordinary savings accounts needs more paper work. Whenever there is a scrutiny by tax authorities on this savings account, it would need more efforts to establish that the credits are from foreign earnings.