Google still dominates by far and is improving technically all of the time.
Yahoo is almost over, their searches have decreased in quality over the past year, and there is a likelihood of Micro$oft buying them out again. Yahoo refused the first time, now they are desperate and losing their founder. This seems a weak negotiating position, so Micro$oft will be able to buy them for peanuts, just like they usually buy companies. Yahoo's engine (Inktomi) has not been improved upon since it was sold to start-up Google. Google have clearly beaten Yahoo. Note to self - if I invent something clever, I must not sell the technology out-right and still try to run a business based on it. That would be like Mozilla making something brilliant and open-source (Firefox 2) and expecting Micro$oft not to compete (IE 7).
Ask are aiming themselves at being useful to women, I do not know how searches can be gender-relevant, and I would have thought women would like to see as many search results as men. Weirder still, they might become Ask Jeeves again now that the trademark has been sorted out. What exactly is the point of adding in an expensive cartoon butler and making the web address longer to type?
There is also Wolfram|Alpha which is a very technically innovative search engine. They are keeping all their AI quiet, which is very sensible. I just hope it does not become SkyNet.
The newest cool feature search engines can have is the Twitter/Friendfeed-like live searching engine. Twitter and Friendfeed have their own live searching engines, but the two services are not primarily focussing on being search engines, at least, at the moment.
In a shrewd tactical marketing move, Micro$oft call their already-failing search engine LiveSearch, yet it is not actually live, i.e. “real-time”, it just spiders through web-pages like Google did. This is 20th-century advertising at its best, it could be called LieSearch.
Anyway, both Scoopler and Yauba are very clever live real-time search engines in the best way possible. Both need JavaScript enabled to make their pages work, but use the latest programming technology and internet standards in a very useful way. Both are well worth a try.
You might like Google for searches, but both Scoopler and Yauba are well ready to be very good competitors. Both clearly technically out-perform Google's results in terms of current relevance.
The new guys' links are:

• Scoopler.com
• WolframAlpha.com (invitation required)
• Yauba.com

P.S. To any lawyers bothered about my blog, note the careful use of conditionals to avoid accusation.
Please let me know what you think of them, the search engines, not lawyers.