He currently doesn't own or fly his own plane, but he does use a plane (which he's rebranded with an Obama logo scheme) for the travel demands of the campaign season. "Although Senator Barack Obama flew on a variety of aircraft during the long campaign season, from March through June 2008 he primarily used a Boeing 757-200ER aircraft chartered from (and operated by) North American Airlines as his campaign plane." Here's a picture:
http://msgboard.snopes.com/politics/graphics/obamaplane1.jpg Source:
http://www.snopes.com/politics/obama/airplane.asp