What were the long-term effects of mongol rule for eurasia?

Negative Effect: 
1) Population dropped because of how Mongols wiped out entire towns and heavily depopulated areas, as well as damaging the land and taking away livestocks.
2) Diseases spread quickly with the Mongol conquest, in which it spread from Asia all the way to Europe. One example of disease is the Black Death, which affected ~1/3 of Europeans.

Positive effects:
1) Mongols, while wreaking havoc themselves, actually gave peace inbetween people groups after they were conquered.
2) Silk Road, was reopened, this time instead of Roman soldiers, Mongols protected the travelers and traders.
3) Russia: Russia was unified because of the Mongol invasion. Before this, Russian people usually lived in independent groups.

Neutral Effect:
Gunpowder: Mongol's use of gunpowder changed the way war worked in the West. In the centuries to come, Europeans would improve and research this weapon, which would lead them to conquer lands centuries later (Age of Exploration)

hope this helps