The campaigns that reached central Europe: Kalka, the destruction of the Rus principalities, Legnica and Mohi.
In 1223 a Mongol reconnaissance force destroyed a combined Rus and Cuman army at the Kalka river and then rode home. Fourteen years later a real invasion arrived, and within four years the Rus principalities had been systematically dismantled, Poland and Hungary had been beaten in the same week, and Mongol scouts had reached the Adriatic.
The campaigns are studied because they were extraordinarily well executed rather than merely large. The Mongol armies operated in separate columns across hundreds of miles and arrived where they intended together; they took fortified cities that had never fallen; and at Legnica and Mohi in April 1241 they defeated two entirely separate European armies two days apart.
What stopped the advance was not a battle. Ögedei Khan died in December 1241 and the commanders withdrew east for the succession, and the invasion of central Europe simply ended. Whether it would have continued is one of the genuine unanswerable questions of medieval history, and the archive says so rather than guessing.
The Rus principalities did not recover their independence for two centuries. That, rather than the raid into Poland and Hungary, is the lasting consequence.