Although I seldom use their search engine directly since they focus more on searches in Russian, I can confirm that it works very well. They also have, among other things, better maintained and more detailed maps of ex-soviet countres with better traffic jam and accident tracking, an EXTREMELY convenient product search that lets you specify an insane amount of properties and features to pick the most fitting item that exists on the market and then find a good rated and cheap place to buy it, a great multilingual online dictionary and a convenient online storage service which has existed far longer than Google Drive. Their web pages have a simple, consistent and concise design, their ads are few and non-intrusive, and, on top of all this, the company has an almost cult standing among many tech students for its high wages and free CS and data mining school where they teach interested people in-depth data mining, artificial intelligence, algorithms and many other related and not-so-much things.
Why do I mention all this? First, to confirm that they are popular for a very good reason and, second, because most of their services use Internet data mining techniques to gather results, so if you live in CIS, chances are you are hooked anyway and you generate many internet searches indirectly even if you don't use their search feature. Unless Google pays as much attention to foreign countries as it does to the U.S. and keeps expanding its services, it should not be surprising to see sound local competition in some countries.