Surely the force of gravity depends on the mass of the object. Since acceleration and therefore force is directional, the direction of the massive object is also relevant. At the centre of the Earth, the force of gravity is operating equally in all directions - equivalent to zero-gravity.
As you approach the centre, the downward force of gravity decreases at an increasing rate, because the amount of mass behind you is increasing ever more rapidly (even assuming you are falling at a constant 'terminal velocity') and the mass 'ahead' of you is shrinking at the same rate.
Air resistance remains fairly constant however (does it not?). If (the magnitude of) the force of gravity is a determining factor in 'terminal velocity' (is it? - I don't know), this will result in a decrease in the velocity of your fall. If this is the case, you will come gradually to a halt at the centre, floating there in zero-g. If it is not, then you will 'bungee' back and forth through the centre in an ever-diminishing oscillation until finally coming to rest there (as other posters have surmised).
The same, or even more than that would be 'below' you, so there is no chance of going in the 'upward' direction.
And as far as my knowledge is concerned, I feel that Earth attracts everything to it's center (the core) and so going back to the surface seems practically impossible.
Of course gravity will never return you to the surface, and I never said it would. But I am confident that the attraction is exerted by the mass in general, rather than the centre, as outlined above.
This raises an interesting question in my mind. If the hole you fall through is drilled equator-to-equator (never mind how to keep the ocean out lol), does centrifugal force from the spinning of the Earth come into play, to slow you down quicker?
