Stars twinkle , planets don't ?

Just to be more clear lets first count the types of objects in the night sky:

1. Stars
2. Planets
3. Artificial satellites
4. Natural satellites (moon)

There are other objects like nebule and star clusters etc. but let's for the time being ignore them.

Now, out of these all the objects exceptstars do not twinkle or blink as you mentioned. So the stars  that you may observe as not to be blinking may be any of these other objects, basically planets or artificial satellites.

The twinkling occurs because of the combination of two phenomena. Firstly, the light from all these objects undergo multiple refractions as it passes through the earth's atmosphere. It may lead to different apparent position of the object, depending on the final direction from which light enters our eyes after multiple bending due to refraction.

Now, the second phenomenon which makes the stars twinkle but not any if the other object is, the size(say diameter) to distance(from earth) ratio of these objects. In case of stars the size to distance ratio is very small, making them just like apparent point sources. If we trace the final Ray entering our eyes it may trace back to different apparent positions everytime( different from actual star), since the earth's atmosphere is not constant and has many local disturbances due to which direction of refraction of light keeps varying.

Where as if we consider other objects like planets or satellites, the size to distance ratio is large. So even if we retrack the final refracted light, the apparent position it maps to is almost the same as the actual source position. Hence we get almost a constant image of such nearby objects.

One more thing that is important is position of stars in sky. The stars near horizon appear to twinkle more than the stars overhead, since the starlight has to travel larger part of atmosphere undergoing more refraction though locally changing medium.

Light from the Sun takes about 8 minutes to reach us, light from Pluto takes about 5 hours, and light from PROXIMA Centauri the nearest star - takes 4 years! Light from ANTARES the brightest star in the constellation SCORPIUS - takes 550 years to reach us. We can see how distances to stars are so huge when compared to the planets.

Stars are so far away from Earth, they appear only as pinpoints of light. And as this pinpoint of light passes through Earth's atmosphere, it is refracted multiple times by the various temperature and density layers of the atmosphere, changing directions very slightly appearing as a twinkling light to us. By the way, the scientific name for the twinkling of stars is stellar scintillation.

Planets shine more steadily because - they’re a lot closer to Earth and only reflect Sun's light - and so appear not as pinpoints, but as tiny disks in our sky. You could see planets as disks if you looked through a telescope, while stars would remain pinpoints even through powerful telescopes. The light from these little disks is also refracted by Earth’s atmosphere, but they are so much larger than the pinpoint of stars - so the twinkling is effect is not seen. However, we might see planets also twinkling if we spot them low in the sky just over the horizon. That’s because, in the direction of the horizon, you’re looking through more atmosphere than when you look overhead.