Do all planets have a molten core? As we know, according to Wikipedia on Earth's inner core:


  The Earth's inner core is the Earth's innermost part and according to seismological studies, it is primarily a solid ball with a radius of about 1220 kilometers, or 760 miles (about 70% of the Moon's radius). It is believed to consist primarily of an iron–nickel alloy and to be approximately the same temperature as the surface of the Sun: approximately 5700 K (5400 °C).


Now the question is, do all planets have molten inner cores?
The short answer is no. Take Mercury for example in this comparison of Earth Mercury core. Mercury is thought to have a liquid outer core and solid inner core. The gas giants like Jupiter are thought to have a relatively tiny rocky core but the convective motion in the metallic hydrogen is what gives them the strong magnetic fields.  

See also: Is Mercury&#39;s core liquid? for more on Mercury's core.