Anything I say will sound extremely cheesy and contrived if I try to be "witty" or "smart", so I'll just say what I'll use it for if I win.
1. Gaming. It would be really nice to move on from this 9800 GTX+ I've been using the past couple years, even though it served me well. It just can't run all the latest and best looking games out there well enough on high settings. Games like Metro 2033, Mafia II, and soon to be Crysis 2 and Deus Ex Human Revolution.
2. I'm a digital painter, and anyone who has ever tried digital painting at high resolutions in photoshop, or just doing any kind of work on a high resolution image, knows that it can get really sluggish when doing certain tasks, such as using a large brush, smudge tool, or even zooming in and out of the image. Photoshop uses GPU acceleration, and while my 9800 GTX+ does an OK job, it just can't cut it on really high resolutions. So, winning the system would really help with that.
3. As a hobby, my brother and I use a program called Blender. It's a really powerful 3D modeling and animation program. Again though, when working at high polygon/subdivision levels, it can really slow down. Having a better system would help with the working on the 3D objects, and also rendering the final product.
That's what I would use it for. Thanks for the contest and good luck everyone.