I was just thinking today of a proposal I read about several years ago to send an unmanned probe to the Earth's core. The geological applications would be obvious. We'd finally be able to observe the core up close instead of merely speculating about it.
The plan is surprisingly simple, and another wonderful application of nuclear bombs. First a large-scale nuclear bomb (on the order of several megatons) cracks a hole in the crust. Into this hole, we dump somewhere between 100,000 and 10,000,000 tons of molten iron and a probe about ten centimeters across. The load of liquid iron would sink into the Earth, carrying said probe with it, enabling it to reach the lower levels of the Earth. Communication with mission control would be achieved with acoustic signals (as in the original paper) or neutrinos (my idea). This requires no technology we aren't in a position to develop and would have a cost comparable to many space explorations.
The scientific payoff would be colossal. I'm sure such a project would challenge our ideas about the interior of the Earth, perhaps as much as the first space probes radically changed our understanding of other planets. Though perhaps it may be done on the moon or Mars before trying to do it on Earth.