This morning, Hitwise came out with its search market share numbers for May, 2008. In the U.S., Google was up slightly to 68.3 percent percent versus 20 percent for Yahoo and 5.9 percent for Microsoft. All the fighting over the fate of Yahoo cannot be helping matters. In the month of May, Google gained 0.39 points from April, while Yahoo was down 0.33 points and Microsoft was down 0.37 points.

In the UK, Google’s market share actually slipped as much as it gained in the U.S. (0.39 points), but it is even more dminant there with 87.3 percent marketshare, according to Hitwise.

For April, ComScore had the trio’s U.S. market share at 62 percent, 20 percent, and 9 percent, respectively. And it has Google’s UK market share for April, 2008 at 74.4 percent. While the numbers may be different—everyone has their own methodology—what you want to look at are the relative trends. Comscore has not yet released its May search market share numbers.

What’s even more telling is that Google is winning the vertical search game as well. Hitwise breaks out what percentage of overall traffic in key categories comes from search in general, and Google specifically. For instance, 46 percent of all traffic to health and medical sites in the U.S. comes from search engines, 31 percent from Google alone. For travel sites, it is 35 percent from from search overall (24 percent from Google). For shopping sites, 25 percent from search (17 percent from Google). News sites get 22 percent of their traffic from search (15 percent from Google). Google’s biggest market share gains (as the primary source of traffic over the past 12 months) were in online video, sports, business and finance, entertainment, social networking, and travel.