What are the spiky things on the back of the Antonov-225 vertical stabilizers?
It appears to be the extension of the aerodynamic fairing between the vertical and horizontal tails (note that the horizontal tail extends outside the vertical one). It can be seen more clearly in the following image.


Image from diecastaircraftforum.com. Original image appears to be from airliners.net

This type of fairings (usually called bullet fairings) are found in 'T' tails and other types of tails (like cruciform tail) where two surface intersect each other at right angles and are used to reduce interference drag (and flow seperation). For example, the following image shows the fairing in C-141 Starlifter, an aircraft with 'T' tail.


airplanesofthepast.com