Why standing wave is needed in microwave oven? In microwave oven, standing wave is created in chamber by reflecting from metal surface. Do we create it intentionally? Is there any special advantages of it? 
 A: The chamber is designed to be a microwave resonator . The first and foremost reason for this would be that it would not be desired to radiate these frequencies out into your living space, as they can heat biological material. For the same reasons, the door has a window with a mesh over it. The wavelengths of the radiation can not escape and enter our eyes, which is more sensitive to this radiation than our skin is. The mesh however allows optical wavelengths to pass through and we can observe how our cooking is going. 
Secondly, it would be wasteful to radiate this energy out of the chamber. With a resonator, the energy is kept inside and thus the efficiency of the microwave oven will go up. 
A: The walls of the chamber constitute a boundary where the electrical conductivity of the metal forces the amplitude of the wave to zero. Any time you create waves of a fixed frequency inside a closed boundary, the steady state will be a standing wave pattern.
https://en.wikipedia.org/wiki/Standing_wave
A: In microwave oven, standing wave is created in chamber by reflecting from metal surface.
We get a standing wave as a natural consequence of how a microwave works. Since a microwave is a resonating cavity, a standing wave will naturally form.
As Solomons answer says:

Any time you create waves of a fixed frequency inside a closed boundary, the steady state will be a standing wave pattern.

Do we create it intentionally?
It arises naturally from how a resonant cavity works, but it does have disadvantages that have to be engineered around.
A standing wave can causes hot spots and cold spots in the food.
Older microwaves tried to break this standing wave by spinning a reflector at the top of the microwave. This broke up the standing wave, note the mode stirrer:

Some microwaves hide this behind a plastic dome, allowing microwaves to pass to the stirrer without exposing it.
Newer microwaves rotate the food on a turn table to pass the food through multiple hot spots, which is a simpler mechanism. This is also one of the reasons cooking instructions tell you to take the food out and stir it part way.

Is there any special advantages of it? 

Simplicity, it's more effort to break apart the standing wave. Additionally, it's difficult to model the exact standing wave inside the microwave when combined with kitchenware and food given the 3 dimensional cavity. It's much simpler to turn the food. A standing wave also gives us constructive/destructive interference in the hot/cold spots.
You'll also notice in youtube videos generating plasma, that the positioning of the glass container can have a big impact on the success of the experiment due to the standing waves peaks and troughs.
For a description of the standing wave and how a microwave works from an engineering perspective, here's a good youtube video
Newer Models of Microwave That Don't Have "Standing Waves"
Newer "flatbed" microwaves don't have turntables, but instead use microwave inverter power supplies in conjunction with pulse-width modulation:

Newer models use inverter power supplies that use pulse-width modulation to provide effectively continuous heating at reduced power settings, so that foods are heated more evenly at a given power level and can be heated more quickly without being damaged by uneven heating

By doing this, you can place much larger items inside the microwave without worrying about significant hot/cold spots
A: To achieve high intensity at low power a resonator with a sufficient quality factor, that is low loss, is used.
A: While standing waves do form inside the cooking chamber of a microwave oven, it is a result of the the radiation being reflected from the inside surfaces of the cooking chamber, but not the reason that foods (and other materials) are heated. 
A microwave oven heats food by passing microwave radiation (in the region 300 MHz to 300 GHz) through it.  Water, fat, and other substances in the food absorb energy from the microwaves in a process called dielectric heating. The microwave radiation raises the kinetic energy of the molecules, which results in a temperature increase.
If a microwave oven is run without an object to absorb the radiation, the energy can be reflected back and forth between the cooking chamber and the magnetron tube, and a standing wave will form. This may result in arcing, and overloading and burning out of the magnetron tube.$^1$
The formation of standing waves results in nodes and antinodes within the cooking chamber. The size (strength) and separation of these is dependant on the frequency and power of the microwave radiation, and the dimensions of the cooking chamber. Heating of the material (e.g. food) generally occurs everywhere within the cooking chamber, but where nodes form, less heating of the material in the oven occurs and where antinodes form, more heating of the material occurs. The rotating plate moves the material around to mitigate this effect. 
