I was surprised that one of my close friends who has been in the software field for more than 5 years had not heard about live search. I truly believe Live is a very good competitor for Google and will have its own space very soon.
Visit www.live.com to start searching. Obviously it doesn't give as many results as in Google search for most queries and might turn up some irrelevant results. But then its still in beta :) and will be improved.
The best thing I like about the Live search is that you can give the priority/settings in which to display the results. For eg, you have the freshness index. If you have searched for a person and want to find his recent entries, you can just goto the advanced tab, change freshness to 100 and query. Recently updated links will appear higher.. Isn't that cool ?
Will update with all the cool features of Live search later but this should get you started.