Hitwise Intelligence took an interesting look at the breakdown of Yahoo's properties today. They come to the conclusion that, even if Yahoo sells off its search division, Yahoo's other properties probably wouldn't be too affected by this, as they get most of their traffic from Google's search anyway. Only Yahoo Image Search, Games, Maps, and News get most of their traffic from Yahoo Search.
Looking at these statistics, it becomes clear that most of Yahoo's properties would continue doing just fine without getting traffic from Yahoo Search. Also, according to Hitwise, Yahoo Search only gets about 12% of Yahoo's traffic anyway, while Yahoo's homepage and Yahoo Mail get a combined 68%.
It's important to note that Hitwise bases its data solely on US traffic. Yahoo is also very popular in Asia. There, these numbers might look slightly different.
As rumors about the future of Yahoo continue swirling around the net, these numbers from Hitwise give us at least some idea that selling only its search business to Microsoft (or anybody else) would still allow the core of Yahoo to continue doing just fine. At the same time, though, the rest of Yahoo would become even more dependent on Google for its traffic.