Nuke that pizza!

First off, before going very far, lets talk about what radiation is. Most people, when they think of "radiation" think of nuclear power plants and Uranium. Of these, there are three types of radiation associated with them.

The first is alpha particle radiation which is the nucleus of a helium atom moving about. This type of radiation is blocked by such little matter as a piece of paper or cloth or a few inches of air. Energy is in the MeV range.
Beta radiation a fast moving free electron. These are much lighter than alpha particles and thus go further - several feet of air or a few millimeters of plastic or light metal. The energy of these electrons range from a few hundred keV to a few MeV.
Gamma radiation is a photon with very high energy (several keV to several MeV). These photons, depending on their energy may be stopped by aluminum foil to several inches of lead.

The radiation that is used in microwaves is most similar to that of the gamma radiation - it is a photon. However, the energy in a microwave oven is far less than that of gamma rays (on the other side of visable light (with respect to x-rays) in the electromagnetic spectrum near radio wave).

There has been a vast amount of research on how microwaves affect the human body - with good reason - we use microwaves everywhere. Microwaves are used from communication (microwave relay towers) to cooking food. Microwave radiation can heat tissue the same way it heats food (food itself is tissue - be it vegetable or animal). Human tissue, when exposed to high levels of microwave radiation can cause a painful burn. Most sensitive to this is our eyes where microwaves can cause cataracts. Directed microwaves can also be used to kill sperm (producing a temporary sterility). One should realize, that all of these injuries are due to exposure from large amounts of microwave radiation. A leak in a microwave oven is much lower.

In comparison, there are a number of other sources of similar RF (radio-frequency) fields. These include television transmitters, airport beacons, mobile phones, power lines, and television monitors themselves.

Yes, RF exposure may cause dangers such as immune responses and cancer (at least they have in laboratory animals and tissue samples). However, given a microwave oven with the door closed the levels are much below the Maximum Permissable Exposure.

One of the great difficulties in linking microwave oven (or any source of an RF field) to cancer is that people are living longer. In 1999, the average life expectancy was 76.7 years. Ten Years prior (1989) it was 75.1, and ten years before that (1979) it was 73.9 years. Going back to 1929 it was 57.1 years. Those extra 20 years of life are ones that genetics really doesn't select for being healthy (after reproductive maturity) and numerous diseases strike. (see ageing and evolution for more on this topic)