Yandex has been #1 in Russian speaking segment of the internet for the last 10 years or so. I use it almost every day. It looks like this expansion into English speaking market is just an experiment, and I'm not sure what they are trying to achieve. It doesn't look like they can compete with Google or Bing.
edit: btw, one of the interesting features Yandex provides and Google still doesn't is street view for Russian cities: http://maps.yandex.ru/-/CFfz7mA.
Interesting - my first search (for hyperion) brought back more interesting results than Google. Not a very scientific study, but that's the first time that has happened to me since I first used Google and searched for java and actually found something about the programming language.
The favicons are a good idea - they do make scanning the list of results a lot easier, even if the overall layout of the page is a bit weird.
I like the favicons being included. Makes it really easy to identify familiar sites.
Overall it feels like a really nice design, but I can't pinpoint why exactly. Might be because Google's strayed so far from the original and simple interface.
Yandex appears to load the favicons from their own cache. If your extension hits the sites themselves, you're leaking the fact that they are appearing in a person's search results to the target sites... and maybe even the query terms, via the referrer header. You should probably mention that fact to users who might not deduce it themselves.
Hmm, started with a vanity search and got totally irrelevant results. Then tried vanity searches with friends names. Again, bad results. Putting the names in quotes seems to do a better job, so the problem doesn't seem to be coverage. Makes it seem like they may not be doing a very good pagerank-like calculation.
edit: btw, one of the interesting features Yandex provides and Google still doesn't is street view for Russian cities: http://maps.yandex.ru/-/CFfz7mA.