I think that the original Grand Theft Auto was the first of its kind.

When GTA3 came out other companies began to copy it and make their own sandbox games with the same themes, except better.

Now GTA4 is coming out, R* have done everything they do well, but seemingly better. Give it a few years and you'll be seeing other companies once again emulating a GTA game and bringing out their own, better version of GTA4.