Interesting answers so far, but I think this one makes the most sense to me:
I look flat, but I am deep,
The ground often looks flat from a mountain, on prairie plains, beach, from the sky, etc.
Hidden realms I shelter.
Animals live underground, caves exist beneath the surface, and human dwellings can extend into the ground as well (basements, tunnels, bunkers).
Lives I take, but the food I offer.
Humans are buried in the ground, but crops also grow from it. Miners are lost to caves, but burrowed animals are also hunted for food.
At times I am beautiful.
Fresh, snow-covered ground is beautiful. So too are grassy plains, and deserts to some. (Many become desktop backgrounds.)
I can be calm, angry and turbulent.
The ground is usually calm, but sometimes earthquakes can occur, which give the feeling of an angry, turbulent personification.
I have no heart but offer pleasure as well as death.
People sometimes sleep or sit on the ground, to rest. They also fall to their deaths sometimes, and die when they hit ground.
No man can own me, yet I encompass what all men must-have.
No one can own the concept of the ground, but humans have fought wars for millennia to claim pieces of it.