Stars tend to twinkle for two main reasons: first, stars are very far away (the closest star is about 4 light-year from the Sun) and are therefore seen as point sources. Second, Earth has an atmosphere. Earth's atmosphere is turbulent, and therefore all images view through it tends to "swim". Therefore, sometimes a single point in "object space" is mapped to several points in "image space", and sometimes it is not mapped at all. Since stars are seen as single points, they sometimes seems brighter, sometimes even seems to disapear.
If you look at it in another planet of our solar system, it will depends on the planet's own atmosphere. If you look at stars on Mars, the atmosphere being very thin, the stars won't twinkle that much. Same for Mercury. On Venus, the atmosphere is so thick than you won't see anything apart from the atmosphere itself (if you are not crunched by the atmosphere pressure, by the way...).