Forest, ocean and jungle are the main counters to mongols. Mountains help too, so long as you don't be retarded.
Sabutai once took his scouting army over a mountain, but messengers beat his army and warned the countries over the other side. The countries banded together and formed armies waiting for them. With the back to the mountain, Sabutai would have probably lost. So he paid off one country to leave, then crushed the one that stayed. Then he rode down the army he paid off and took his gold back.
Anti-horse tactics are the name of the game with mongols, really. They had the power of mechanised infantry before mechanisation, since they had speed and range. I'm a little upset that no-one tried just mass producing caltrops. Just make like 4 million caltrops, and litter them behind you as you run like fuck from the mongols. The horses go down and you keep running. Without horses they can't do shit.