Are we heading that way? Yes, for sure.
Search is not supposed to be something independent of the rest of your web experience, or actually you digital experience. You are going to be able to access search from any device or environment without actually having to go to a search engine.
Imagine you're typing away an article for your photography blog. The intelligent environment you're in is already aware that you are writing something for you blog, because it has seen patterns and features develop over time. You highlight something and summon Google. It does something pretty cool. It goes out with the highlighted words as a query, but already has the context of the query, because of it knowing all about your writing for your photography blog.
It rushes out, and visits all the top results. These results are dependant not just on the keyword phrase but also on the other variables gathered from your intelligent environment. Then it pulls out all the key concepts and information and writes you a summary to answer your question. You can "repair" the results by typing something like "No, I meant..." or "Perfect! Tell me more about the canon". And off it goes again. Or "Let me see the top 5 documents", or "Show me related information",...
From a mobile device, you could summon Google during a conversation with someone for example. Imagine you're trying to figure out where the closest restaurant is to you both. You summon Google and ask it, where's the best place for us to meet, she's vegetarian". You can request an answer to a question like "Did Angelina Jolie really bungee jump yesterday?" and get a response such as "Yes she did. She jumped off a bridge in New Zealand".
I look forward to summoning Google and saying "Remember when I was writing that paper for that conference? There was a quote by x about y in it, what was it?"..."That's right, who else said something about that?"...
Google becomes a backend system. Gasp! No but there is nothing more natural than for the engine to be in the background. I think that conversational systems removed from search are fun toys, but their real use is in information retrieval. Once you start getting used to having all your information at your fingertips as and when you ask, you are also going to get used to conversing with the system pretty quickly.
For this kind of thing of thing to work you will need strong summarization systems, natural language generation and understanding, and machine translation, personalization, machine learning also, not to mention all the other supporting technologies without which it could never happen. Luckily these are all under development right now.
One of the most interesting questions I believe is "Does your behaviour change now that the search engine is conversational in nature?" - Does it become your friend, do you get attached to it because it shows human qualities, or do you treat it like a tool? Does the way that you search change now that you no longer actually go to a search engine web page? Are you more focused, more specific, more vague?
Hummmm....so how are businesses going to take advantage of the search market then? Clearly ads are still going to be served up, but how do you make sure the clever agent like your content most of all?
Google discuss the more immediate future of search here.