Why the comets can cross the orbits of planets? Why are comets able to cross planetary orbits without colliding with the planets - Why is the comets' orbits elliptical, intersecting all the other planets' orbit.

Why don't they get attracted by the planets when they are in their orbit. 

Or, why doesn't the force of gravitation from the planets not attract or compel the comet to rotate around them.
There are several reasons, the main ones are:


The orbit of some comets may appear to 'cross' a planetary orbit when viewing the solar system in 2-dimensions, but their orbit does not lie in the ecliptic plane (that the planet orbits follow).  An example is Comet Hale-Bopp:




Analogous to why Pluto won't hit Neptune despite their orbits appear to 'cross' in 2D representations.

Image source: http://spiff.rit.edu/classes/phys235/comets/comets.html


Some comets do have orbits on the ecliptic, particularly some short-period comets, such as Comet Encke:




Same image source as above

However, it is important to note that the chances for the comet and planet to be in enough of a vicinity to each other to result in the comet being 'captured' by the planet is low - so if the planet is not nearby, the comet can just keep on going on its normal orbit.

Though we have witnessed if a comet gets too close to a planet, when Comet Shoemaker-Levy 9 got caught in Jupiter's gravitational field, tidally fragmented and eventually collided in 1994.

in terms of whether a comet could be captured in orbit around a planet, this has been addressed as answers to the question "Can a comet orbit a planet?".