bookend and wildwood are, of course, correct in their assertion that water would never reach anywhere near the centre of the earth, even if you could drill right through,which is impossible.
However, to answer the question in the spirit it's written,
If the earth was a solid, cool mass and a tunnel from side to side was possible, the water would fall under the influence of gravity, accererating all the way to the centre of the earth, then begin to slow as it passed the centre.
It would continue to decelerate until it almost reached the "hole" at the other end, air friction would have slowed it down and it wouldn't quite see the light of day at the other end. it would then start to fall back down the hole again then it would ossilate back and forth reaching up the tube less and less each time until it stopped finally at the centre of the planet