Final frontier altitude
A reasonably accepted 'official' minimum altitude for space is 100km. SpaceShipTwo is intended to reach 110km, so there is enough of an excuse to call it a space ship. It is carried into the air mostly horizontally, and after launch goes up, falls down and when it gets deep enough into the atmosphere, it levels out and glides home.
When going to orbit, a rocket goes up to get out of the worst of the atmosphere, then leans over to almost horizontal. If it did not go up first, air resistance would melt it long before it went fast enough for orbit. When in orbit, a space ship has a little energy because of its altitude (>150km) and lots of energy because the velocity required to stay in orbit. SpaceShipTwo has almost no velocity at 110km, so it has no chance whatsoever of reaching orbit. Even if it did go fast enough, there is enough atmosphere at 110km to bring it down before it goes around once.
It really is the absolute minimum required for the widest definition of a space ship. The maiden voyage will be in late 2009... well, RSN anyway.
Virgin Galactic are working on a cargo launcher called LauncherOne. It is intended to take 230kg (≈two humans, one space suit and no ride home) to low Earth orbit. LauncherOne gets carried by White Knight Two, just like SpaceShipTwo. The first test flights will be in late 2016. If it is not very late, it will meet a much stronger definition of a (cargo) space ship.