The weirdest Google competitor I've seen so far is ChaCha, an assisted search company. What that means is that you have a text-chat conversation with a person on the other end of the search engine, someone who's supposedly an expert, and they help you find the info you're looking for.
I tried finding a hotel in Austin for the South by Southwest conference by entering "sxsw," and I was connected to a nice person in the "conditions and diseases" category. A poor start to my ChaCha experience, but she did a yeoman's job of pulling down hotel listings for Austin even if she didn't have any expertise in the area. In a second, more specific search, "South by Southwest hotel recommendation," I quickly identified that my guide had no experience with the conference, but he transferred me to another guide (cool feature), who sent me some good hotel advice links (Expedia, TripAdvisor, and so on). But this third guide had also never been to the conference.
I could have found what I needed more quickly and more accurately on Google (or on ChaCha's unassisted search). Although I had a lovely time talking to some people doing their best to be helpful, ultimately it was a waste of time, mine and theirs. If ChaCha were actually able to direct me to someone who had been to the conference and knew which hotels were good and which weren't, I'd have a different opinion.
And that's the whole issue with assisted search. When we want expert advice, can we really expect to get it from somebody who's making maybe $10 an hour (the top end of what ChaCha pays out to its search assistants) and is handling dozens or hundreds of categories? Maybe if this tool were somehow blended in with a wisdom-of-the-crowds engine such as inChorus it would work; or as TechCrunch notes, with Amazon's Mechanical Turk (Amazon's Jeff Bezos is an investor in ChaCha).
Source: A recent CrankyGeeks videocast I appeared on. Skip to 07:20 for the search engine segment; Sebastian Rupley tipped me off to ChaCha on the air.