With your current code you'd need some looping mechanism to iterate the If statement over each possible value for i, j, and k.
If you just want to replace every non-zero element with 1, however, I would just do the following (using Replace, and targeting non-zero elements):
In[1]:= x = {r, t, phi};
In[2]:= R = {r Sin[t] Cos[phi], r Sin[t] Sin[phi], r Cos[t]};
In[3]:= e = Table[D[R, x[[i]]], {i, 1, 3}];
In[4]:= g = Simplify[Table[e[[i]].e[[j]], {i, 3}, {j, 3}]];
In[5]:= ginv = Inverse[g];
In[6]:= capitalGamma =
Table[Sum[
1/2 ginv[[i, l]] (D[g[[l, j]], x[[k]]] + D[g[[l, k]], x[[j]]] -
D[g[[j, k]], x[[l]]]), {l, 3}], {i, 3}, {j, 3}, {k, 3}];
In[7]:= Replace[capitalGamma, (x_ /; x =!= 0 :> 1), {3}]
Out[7]= {{{0, 0, 0}, {0, 1, 0}, {0, 0, 1}}, {{0, 1, 0}, {1, 0, 0}, {0,
0, 1}}, {{0, 0, 1}, {0, 0, 1}, {1, 1, 0}}}
No doubt other solutions exist, though.