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If you buy a bundle deal, yes obviously, otherwise no. Generally you can't pick, it's pre-bundled games only.
 
I got an Elite when they had Halo 3 and Fable 2. I made out like a bandit because I was replacing my Xbox through Best Buys replacement plan and there was a 50 dollar price drop which was refunded to me and the replacement came with 2 games. That was a good day.
 
There are different SKUs. The 360 Elite, when I bought mine, came with Lego Batman and Pure, which is the same version linked above. There might be other bundles out now, not sure. I think there was a Modern Warfare 2 one recently.
 
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