Google still reigns supreme of course, followed by Baidu and GoogleMicrosoft has been pouring billions into Bing and, more recently, into hate-filled ad campaigns, to get a piece of the ad money pie that Google gets to savor almost all by itself.
Microsoft's search engine has been making some progress, but it seems that others with much smaller budgets are growing a lot faster than Bing.
According to the latest comScore numbers, globally, Bing has dropped to the fifth spot, overtaken by Yandex. In both November and December 2012, Bing saw fewer queries worldwide than Yandex, which only serves Russian-speaking markets and Turkey.
Note that this is in terms of search volume, not users, Bing still has a lot more users worldwide than Yandex, but Yandex gets more searches because its users are more loyal (and have fewer options).
Google is still at the very top, quite obviously, and Baidu, the largest search engine in China, is second. Yahoo comes in third, followed by Yandex and Bing.
It's not really a competition though, Google saw 114 billion searches in December, Baidu 14.5 billion, Yahoo 8.63 billion, Yandex 4.844 billion and Bing 4.477 billion.