Javascript: Create a 10x10 array of 1s
Javascript, 34 bytes
for(r=[b=[i=10]];i--;r[i]=b)b[i]=1

Since it's apparently OK to make the rows equal by reference, I guess it's apparently OK to rely on that fact. This helps us shave off one for-loop by building the table at the same time as its rows. So, here's my new contestant.
Since r[0] and b[0] are overwritten during the loop, they can contain garbage. This gives us another free execution slot to shave off some commas. Sadly, r=b=[] won't do, since then they are equal by-ref.
Also, it scales well (99x99 is still 34 bytes), doesn't require ES5 (the new functions have terribly long names, anyways), and as a bonus, it's unreadable :-)