Main searchers

Yandex – ~49% of RuNet users
Google - ~45% f RuNet users
Mail.ru - ~5% f RuNet users
Others - have a negligible percentage of f RuNet users

* If you count phones, then Google has bypassed Yandex, just tying its search on Android.
At the moment, Yandex has submitted to the antimonopoly service, the case goes through instances.

Main Searchers:

Yandex - The leading search engine in Russia
Google - The leading search engine in the world
bing - Search from Microsoft.