Can a plane fly without the Vertical Stabilizer?
The plane will probably crash.

The vertical stabilizer provides stability in yaw to conventional aircraft. Aircraft such as the B-2 manage to provide stability through computer control, and aircraft such as the Northrop flying wings are designed to fly without one. But if an aircraft designed to be stable using a vertical stabilizer loses that surface, it will be very difficult for pilots to stabilize manually with the remaining systems. While roll and differential thrust will both affect yaw, they will both be slower to react than a rudder, especially in a large aircraft like an A380. This can also damage the hydraulic systems, making it more difficult to control the remaining surfaces.

If experienced test pilots are at the controls (as in the B-52 incident below), or if the failure is anticipated and trained for, it's possible that the aircraft would be controllable enough to land safely. However, as the incidents below show, this kind of failure does not happen often, and can easily exceed the crew's ability to control the plane.

Examples where this has happened:

Japan Airlines Flight 123 lost most of its vertical stabilizer when the rear pressure bulkhead failed. Despite also losing hydraulic systems, the pilots managed to keep the plane in the air for a while, but ended up crashing into a mountain.

American Airlines Flight 587 lost its vertical stabilizer when the pilot's rudder inputs over-stressed the structure. It crashed shortly after.

In 1964, a B-52 lost most of its vertical stabilizer due to extreme turbulence. The pilots were able to extend air brakes on the wing tips to provide some stability. The Air Force sent up a chase plane to help guide the pilots, and provided engineering guidance from the ground. The crew were able to bring the plane back for a safe landing (see a video). There were at least three other instances where the vertical stabilizer failed on B-52's, all ending with the loss of the plane. This particular flight was conducted with test pilots to intentionally fly through turbulence, recording data to help understand the failures on the other aircraft. However, the flight encountered unexpectedly severe turbulence, leading to the separation of the vertical stabilizer.