Actually, the "Barbarian mongols" are one of the funny cases where history was written by the loosers.
The Mongol policy was to demand surrender, and, if that was refused, beat their opponents into submission. If their opponents put up a very hard fight, or if they attacked them after "faking" a surrender, their opponents were executed.
A number of the Russian principalities like Ryazan or Kiev fought them, and lost. Novgorod on the other hand (later also Muscovy) surrendered and gained fairly wide ranging autonomy.
On an even more intersting Sidenote, Dschingis Khan actually had a valid Casus Belli for his inner Mongol (Other khan stole and raped his wife), Chinese (ambassadors seriously maltreated, Chinese supported his enemies and were caught) and Khwarezmian (Local beylick killed about 100 Mongols from a trade expedition in some particularly nasty ways) campaigns.
When the Islamic Khwarezmian (and later the Kalifate of Bagdad) asked other moslem states to support them in defense of Islam, the help was refused, with the Muslim theologists claiming that the "Mongols" had due cause and that they were "fighting against the King/Sultan/Kalif in question not against Islam".
Apart from Hulagu Khan, (who was not a very pleasant person anyway), most Mongols were very tolerant for the time they lived in.
Batu Khan allowed widespread autonomy for the Russian orthodox church, provided they dont proselytyse amongst mongols, the later Crimean Khanate was propably the only Muslim state with a significant alcohol industry.
The early Crusaders for example, did usually not ask for a surrender (much less actually respecting it if it happened) and often massacared their "non Christian" opposition regardless of their particular conduct.
The later crusaders asked for surrenders but did not take them serious, like in the battle of Adrianople.
Considering Mongols in the Holy land, the Mongols advanced quite a bit, but the Battle of Ain Jalut ended their advance and prevented any serious efforts of cooperating with the remaining Crusaders.