Randall Munroe (author of xkcd) addresses this question in his excellent book "What If?", covering what would actually happen (basically a nuclear explosion), w

Randall Munroe (author of xkcd) addresses this question in his excellent book "What If?", covering what would actually happen (basically a nuclear explosion), what would happen if it was somehow kept magically at the same density without exploding (it will end up oscillating around then settling at the Earth's core), and finally and most interestingly what it would be like if you could keep it near the surface and attempted to approach it.