Do aircraft owners need to purchase insurance?
Aircraft insurance for personal aircraft is not legally required by any part of the US FARs, nor to my knowledge is it required by any state government, though I'm only familiar with New York in that regard. (As you'll note from the Wikipedia page you linked to, not all states require automobile insurance either, though most do now...)

Aircraft insurance is most directly comparable to marine insurance.
It's generally required by:


Your lender (if you didn't pay cash)
They want to be sure you have hull coverage so if the plane is damaged they still get paid.
Your FBO or Airport Management.
As a condition of having a tiedown/hangar most FBOs require some form of liability insurance in case you taxi into a building or another plane.
Good old-fashioned common sense.
A light piston single is unlikely to take out a building, but if you have an incident costs can rack up fast. Having someone else to step up and pay those big bills is beneficial.