Nope, the 8800GT was a pretty darn good card for its time. You wouldn't see any increase of performance if you went with a 9600GT. You probably would actually lose performance. If you like Nvidia, try the 9800GTX, if ATI the 4850. Both good cards.
You should stay with your card and get a GTX 260/280 when the prices drop.
I'm upgrading from a 7600 GT because mine died so it will be a big difference for me, and the 9600 GT is more than enough to run the latest games on high settings (like crysis for example).
If you must upgrade from a 8800GT (still a fine card), I'd recommend getting at least a 4850. IMHO, the best bang for your buck card on the market right now. Sweet spot, if I've ever seen one (along with the cheaper, less powerful 8800GT).
no... if your going to upgrade, then make it a significant upgrade. the 4850 is perhaps 30% better? really not worth getting right now. go with at least 4870 if your must upgrade.