Which kinds of FET have a body diode
Even though the body diode in MOSFETs is often drawn as a physical diode next to the MOSFET, it's not actually a discrete building block of a MOSFET. It is a 'parasitic' element that exists inherently because of the silicon build-up of a MOSFET. There are no MOSFETs without body diodes, it's a fact of life.

That also means that this body diode isn't actually a purpose-made diode. It doesn't quite behave like either a signal or power diode and it has fairly poorly defined characteristics. However, it also means that it doesn't have reverse leakage like a traditional power diode. It's part of the entire package, so the datasheet usually defines an overall reverse leakage figure. For instance, completely random power MOSFET datasheet:

http://www.st.com/web/en/resource/technical/document/datasheet/CD00002217.pdf

Here, on page 4/13, it states a 'zero gate voltage drain current', i.e. leakage current. It has a typical and maximum value of 1 and 10µA respectively at Vds=max. That is what you have to design for.