Yes the other planets are also density stratified such that the deeper one goes the higher the density. The heavy things fall to the center!

As far as I know, we know very little about what layers other planets have.

It is possible that they have them, but we have not been able to determine this for sure. Scientists discovered the layers in the earth by sending sound waves through the earths crust and monitoring how long it took for the sound to get back. Different layers of material will allow the sound to travel at different rates. So, if we did this kind of test on other planets, we could determine if they had layers as well.

Planetary scientists are pretty sure that Mercury, Venus and Mars also have these layers. Their cores are mostly made of iron and their mantles are probably made of similar basaltic material. Their crusts are made up primarily of basaltic rock versus the Earths crust which has so many different rock types (granite, sedimentary rock, etc.)

Mercury no longer has a molten mantle and is completely solid. Venus probably still has a molten mantle because its entire surface is relatively recent in geologic terms, about 500 million years old. (Earth is 4.6 Billion years old). Mars may also still have a molten mantle but is fairly geologically inactive meaning it has no plate tectonics, earthquakes or active volcanoes.

Not just planets have a core, mantle and crust. Several moons in our solar system have them! The Moon has a core and mantle similar to Earths but the crust is basaltic rock. Last but not least, the moons Titan, Triton, Titania and Ganymede have silicate cores (minerals containing the element silicon), mantles made of water and ice, and crusts of ice.
(Thanks to Diane Hanley, Geologist, Science Center of NH)