The answer actually depends on one single point. Money!

nVidia GeForce 9600GT is the new main-stream (budget) card. It uses a G94 processor, has 512MB VRAM and lacks direct X 10.1 support unlike many expected.
Therefore, this has very little to offer feature-wise when compared with G92 (8800GT).

Lets first focus on the performance of nVidia 9600GT.
I wont bother about the FPS benchmark images as they are available in almost every tech-news site. I would rather try to summarize the whole thing and let you guys know what is the best thing to do.

9600GT is:

• almost equal to (but always below of) 8800GT on lower resolutions (<1600).
• slightly below or equal to ATI Radeon HD 3870 (without AA)
• better than Radeon HD 3870 (with AA)
  

Price range of:

• 9600GT is $169-$189
• 8800GT is $199-$200+
• Radeon 3870 is ~$180

Now, if you think about it carefully, you should try to buy a 8800GT (the 512MB one; not the one with 256MB VRAM) if you can.
If you are really short on budget, can't afford $20-$30 more, go for 9600GT.
And finally, there's not much reason to go for 3870 unless you want DX 10.1 support.


On a side note, 9800GTX will be released next month (followed by a 9800GT) and you can blow out any 8800GTX with it for a mere $599.