This one I've been thinking on for a while. What advantage would these have and how frequent were they?

In 15th century Italy, extremely common. I don't know about elsewhere.

I'm reading a book that mentions them right now. Offhand I seem to remember that the author says they are not much use firing while mounted, but their mobility provides a lot of flexibility. He also said that they were more useful as bodyguards in a city than standard heavy cavalry.

I would think loading a cross bow while mounted would prove far more challenging than a standard bow operation.

from wiki:

http://upload.wikimedia.org/wikipedia/commons/2/22/FrenchMountedCrossbowman.JPG
16th century French mounted crossbowman ("cranequinier"). His crossbow is drawn with a rack-and-pinion 'cranequin', so it can be used while riding.

China used crossbows quite frequently in their history and in large numbers, main advantages would be ease of training and range. It was brought up quite frequently in chinese historical records that they were able to outrange their opponents, horsebowmen for the most parts.

It is my impression that the mounted crossbowmen were used primarily as mounted infantry. That is, they rode to the battle and it gave them speed advantage, but fought on foot. But this is a pure speculation.

It is my impression that the mounted crossbowmen were used primarily as mounted infantry. That is, they rode to the battle and it gave them speed advantage, but fought on foot. But this is a pure speculation.

ala Dragoons?

ala Dragoons?

Yes, quite the word I had on mind.