Disappearing object

You give it a collider, and make sure that if it's a mesh collider it's set to 'convex'- because terrain colliders count as meshes, and as such don't collide with other mesh colliders.

Of course, this only applies if you're using rigidbody physics- if you have written your own physics, then you will have to manage collisions manually.

Thanks syclamoth; my player object now stays on the ground!