Weightlessness flight in a huge Il-76 plane in Star City, near Moscow, Russia. The Il-76 aircraft flies 10 parabolas total - each allows for about 25-35s of total weightlessness.
The Russian Zero Gravity flights take place about 3 times a year and can be booked here: http://www.migflug.com/en/jet-fighter-flights/flying-with-a-jet/zero-gravity-in-russia.html
There is also Weightless flights from different US locations - in the ZeroG Boeing 727. But the Russian ZeroG Il-76 is by far the largest weightlessness plane in the world.
The Il-76 is usually used for Cosmonaut training as well as Astronaut and ESA astronaut training from Star City, where they are prepared for the International Space Station ISS. The Il-76 only takes 14 passengers per flight (as opposed to the 36 the far smaller Boeing 727 takes) - so the experience is somewhat more intense and allows for huge space to float in weightlessness.
The Zero Gravity weightlessness flight must be applied for 45 days before the flight takes place. We organize transfers from your Moscow hotel and the whole experience takes a day, including all preparations. You need to do a short medical at your doctor to make sure you are good to go.