What cosmic disaster is most likely to happen? Of all the different ways that the Earth can be destroyed what ways is the most likely that could happen?
Asteroid impacts are a possibility, but a killer asteroid typically affects the Earth every few dozen million years. This would probably destroy all life as we know it, but life will probably nonetheless persist. Statistically, by 500,000 years from now, we should have been hit by an asteroid 1 km in diameter, and 100,000,000 years from now, we should have been hit by one that is the size of the one that killed the dinosaurs. Statistically it's very unlikely we will get one that completely obliterates the Earth, causing it to be completely and utterly destroyed.

Gamma-ray bursts may irradiate the Earth to the point that complex life will no longer be able to survive, and only very resilient organisms like waterbears may live. At some point in the next 300,000 years, WR 104 is expected to go supernova, and if the poles are somewhere around 12 degrees or lower  we could be in the path of the supernova. We aren't 100% sure what its axis is angled at though. Either way, it won't actually destroy the Earth, but just irradiate it.

In roughly 7.5 billion years, the Earth will probably have been destroyed by falling into the Sun, as it engulfs the inner planets. This is nearly certain, but if somehow, the Earth-Moon system were to survive, then 50 billion years from now, the Earth and Moon will have become tidally locked. Then the Sun would extract angular momentum from the system as a white dwarf, and will cause the Earth's spin in accelerate and the Moon's orbit to decay. If this happens, then roughly 65 billion years from now the Moon will crash into the Earth, which would probably destroy it.

Keep in mind that there are many more ways that life as we know it could end, but these are not cosmic disasters, but are geologic and biological disasters, so they are not included. Generally speaking, it's very hard to completely destroy the Earth.