I recently read a great What If essay that argues we'd all be speaking mongolese if the Khan hadn't been gathered unto his fathers at a most inconvenient time. In 1241, having destroyed the Christian armies of central Europe, the Mongol hordes were poised to take Vienna when the messenger came calling them back for the shiva. No Christian army in Europe was a match for the horde; had they continued their march West, the Mongols would have reached Paris.
In short, the West dodged a bullet.
Had the Mongols swept through Europe destroying everything in their path, as was their habit, we'd have no capitalism and no renaissance, no enlightenment and no rights of man, no Yeshivas and no Hasidim, no habeas corpus and no freedom of speech. All the small, fledgling 13th century ideas that, in the fullness of time, grew into what we call "Western Civilization" would have been snuffed out in the cradle. Political and technological developments we take for granted would have been retarded by several centuries - if they ever emerged at all.
For an idea of how the West might have ended up if the Mongol's march of destruction hadn't been prematurely cancled, consider what happened to Islam. The Muslim world met the Mongols in 1240, and much of it was reduced to rubble over the course of a summer. Almost 2 million dead in Nishpaar; 1.5 million in Heret and nearly a million in Samarkand, with many many smaller cities completely obliterated.
Before the horde came, Bagdhad was the world's greatest seat of learning and a place of commerce and art. In six weeks the Mongols reduced this great city to a killing field, murdering over 1 million people, together with the infant Muslim universities and scholars that may have ultimately produced an Islamic Enlightenment, and with it a liberal east.
Oy meh haya lonu.