If you absolutely insist on doing the iteration procedurally, then like this:

f[x_] := 9 Sin[x]/Exp[x^2] - x^2 + x - 1     (* note clearer entry form for the function *)
iterations = 10;
z = {0.2};

fp[x_] = f'[x]      (* pre-evaluate the symbolic  derivative *)

For[j = 1, j <= iterations, j++,
 a = z[[j]];
 z = Append[z, a - f[a]/fp[a]]]

Print[NumberForm[z, 10]]

However, it's better to use a Do expression instead of a For expression, so you let Mathematica take care of the details of incrementing the counter j (the "j++" stuff):

z = {0.2};
Do[a = z[[j]]; z = Append[z, a - f[a]/fp[a]], {j, 1, iterations}]

However, as the answer by Frank Kampas shows, it's MUCH better to use the functional NestList expression: let Mathematica take care of essentially all details of the iteration, that is, of appending each iterate to the current list and incrementing the counter.

But why do you need to implement Newton's Method yourself? The built-in function FindRoot will use it by default:

FindRoot[f[x], {x, 0.2}] // NumberForm[#, 10] &

And if you want all the intermediate approximations, use Sow and Reap:

Flatten@Prepend[
   Last@Reap[FindRoot[f[x], {x, 0.2}, StepMonitor :> Sow[x]]], 0.2] //
  NumberForm[#, 10] &