A lot of people seem to have a terrible opinion of Genghis Khan. This, by and large, is due to European records, which are based strictly on the records and legends from the Middle East, where the Mongols were somewhat less than popular. Accrding to Persian records, at the battle of Nishapur, the Mongols defeated 1,747,000 men. Other records put the battle of Herat at 2,400,000. The simple fact is that there weren't this many people anywhere in the Middle East, as historical and archaeological studies have shown.
In reality, as shown by numerous Asian records, Genghis Khan was a patron of freedom and the arts. Religious diversity, international trade, and free exchange of ideas all resulted from the Mongolian Empire he began.
Genghis Khan also proved an effective governor and was excellent at inspiring loyalty in his followers. Unlike almost any Empire builder before or after him, he died a peaceful death.
In addition, Genghis' methods made sure that anybody showing talent or abilities was allowed to advance to their full potential. Shepherd boys became generals and governors, stable hands became masters of horse.
Contrary to popular images, and directly opposed to European armies of the time, the Mongols under Genghis Khan and his successors did not torture, mutilate or maim. In some cases, they even took particular revenge on cities which had done so to their Mongol captives, particularly in Persia. This is why so many of the Persian records are full of hate for the Mongols, and one of the key reasons Europeans generally have such a slanted view.
With regards to the Mongol use of plague-ridden corpses as siege weapons, this is little but an urban legend. The only document indicating it to be the case also clearly states that it was second hand information even at that time, as such no stock can be put in it. This is in stark contrast to European heroes such as Frederick Barbarossa, who in 1160 at Cremona hurled live children at the walls with catapults.
One of the key reasons so many cities were sacked is that the Mongols, like Alexander and the Romans before them, always punished rebellious populations harshly. Many cities which surrendered without a fight found the Mongols' treatment of them so benign, that they assumed these were not the vicious warriors they had heard of and decided to rebel once the bulk of the Mongol army had left the area. Upon their return, the Mongols usually punished the population, but for their treachery - it was not pointless slaughter.
Even in the Middle East, however, where the Mongols undoubtedly did the most damage, they did some good too. Centralizing trade routes improved the efficiency of the entire system, and they systematically wiped out the hashishin, a powerful group of Muslims from whose name we get the word 'assassin'. The hashishin had been king making for years, and generally exerting undue control over every aspect of the Muslim world through assassination and fear-mongering, and the Mongols put a stop to it.
After the Mongols captured a city, they had a very specific manner of dealing with the inhabitants. Soldiers were killed, for obvious reasons. The rest of the civilians were then emptied out of the city and divided up by profession - emptied out so that the Mongol soldiers could loot with minimal risk and slaughter, and divided by profession so that the skilled laborers (artisans, etcetera) could be put to use in the new Mongol regime.
Mostly this is based on Genghis Khan and the Making of the Modern World, by Jack Weatherford, which is easily one of the most comprehensive works on the subject. The author actually spent years in Asia and the Middle East researching, with a lot of that time spent in Mongolia itself.
It should also be noted that not all sources present the same view. Geoffrey Chaucer in Canterbury Tales presents a very positive view, while Voltaire is quite negative. Since Chaucer is much closer to the time period, I'm inclined to accept his version more readily.