The Core

What Would Happen When The Core Freezes?

Diagram Of The Earth's Inner Layers

The Core of the Earth | 100 Greatest Discoveries

What Would Happen If The Core Froze?

Naked Science - Earth's Core

No More Land, So What Else?

Even though it will take awhile for the land to break down and be gone, you'll still be able to live on the ocean with a ship of some sort. That is until the magnetic field weakens, and is fully gone.
Soon the deeper liquid metal core starts to freeze up. That would result in both the magnetic field, and water dissolving. But most importantly, all air would be lost.

The Next Mars?

Mars had gone through this process a few billion years ago. Because it is smaller than Earth, it froze up sooner. Earth is believed to go through this process of core freezing, and ending of humanity. But not anytime soon.