A lot of Strategic things have been mentioned. Here's my 2 cents on Tactics versus Mongols:

From MTW I learned (and in STW and RTW it is practically the same), that it is the most non-western unit that is the hardest to beat. The Horse Archers. Don't get me wrong, their heavy cavalry is though as hell, but it can be beaten with Spears, Knights and even help from Archers (even more if you play England). Quite conventionally so.
The problem with their horse archers is that at 1st sight you have practically nothing to counter them with. Only perhaps Longbows or other missile troops, but you can't rely on archers alone (dont bring a bow to a horsefight ), not when u face an army that also has heavy cav and other troops to worry about.

There is only one thing to beat them with, and you have to beat them at their own game. Light Cavalry. Heavy Cav they outrun, and spears they go around. Everyone knows what their Horse archers do. They skirmish you to frustration and then when u don't expect it charge into your flanks. Only when u invest in large numbers of Light cav u can chase, corner and attack HA's. It takes a lot of maneuvring, and a lot of stress (the HA-LC battle is bound to take place in an area on the other side of the map where your infantry and Knights are), but if you go into the field without (enough) Light Cavalry, you can beat them in their own game. Taking a defensive stance in woods also helps, with Heavy and light cav on the flanks, as soon as they approach close enough, try to nibble off some of their archer units with cav attacks.