Do stars have exactly sphere shape?
Planets (at least, some of them like Earth) aren't exactly spherical - but what about stars?
Is Sun perfectly spherical, for example? What may be the reasons if it isn't? What about other stars?
No, no stars have an exactly spherical shape. The reason for this is that the centrifugal force of the star's rotation is much greater at the equator of the star than it is at the poles, for the simple reason that the rotational velocity is greater. This greater centrifugal force pushes the equator outwards, stretching the star into an oblate shape. This is called gravity darkening.
Because we have only visually resolved the surfaces of a few other stars, it's not something that is commonly directly observed (though the effect can also be observed from stellar spectra). Regulus is one star that has been observed as an oblate spheroid spectrographically. The image below shows the star Altair, directly imaged using the CHANDRA space telescope. Go here for an animation!
Some stars are also non-spherical due to the effects of a nearby star in a close binary orbit. Much like how the Moon causes tides on Earth, two stars can stretch each other's surfaces. If they're very close to one another, as in the picture below, there can even be mass transfer between them (ref common envelope).