It seems that the trend is that SEO techniques have Google in mind. But what about optimizing for the other search engines like Bing and Yahoo?

I think that it depends on a number of factors but the most basic is where does the majority of your traffic come from. One of my clients was concerned that their website was not performing as well in Bing and Yahoo as it was in Google. But when I pointed out that 85% of their site visitors find them through Google and another 6% were from people who typed the URL directly in, he viewed the Bing and Yahoo results as less troublesome.

The reason why all or at least most of the webmasters and site admins are concentrating over Google is because of the traffic their sites would get after reaching the top spots.

But other engines like Yahoo and Bing too are great and need to be considered.

As we know that Google covers more then 70% of the online market then and due to it the traffic and visitor coming on website through Google so everybody optimize Google for getting top rankings in it in comparison to other search engines.

I wonder with Bing quickly gaining market share, if now websites need to optimize for Bing as well....

I think that regardless of where the majority of your traffic is coming from you have to optimize for the all of the big 3. What you have to be cautious about is attempting to optimize for every site, especially some of the newer ones. There is another thread about a new SE called Glearch that aggregates the results of the big 3 SEs and there are people posting there if anyone knows how to optimize for Glearch.