Is there any privatization in space travel?

no, but there is a competition

http://www.soultek.com/space_privatization/x_prize/x_prize.htm

(at least i think there isn't, we'd have heard about it then)

Richard Branson's Virgin organisation has announced plans for space travel and is taking bookings for tickets.

See the virgingalactic website for details.

US export controls have been reported as possible sources of delay in the past. Presumably the recent (Feb 2007) agreement between Virgin and NASA indicates more recent progress,

Yes there will be when a safe aircraft is availible to transport people.