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Your kids with them get claims if the mother has any to give. Also, it lets you marry for alliances and use concubines to try for genious/strong/attractive children. Plus you get 0.2 prestige/month from per "nubile concubine" (I'm guessing that's when they are below 30 years old or so).
 
You also get a one time prestige bonus for taking a noblewoman as concubine.
 
You can arrest your vassals' wives - you know, the ones with the 'huge tracts of land' - and make them your own concubine. Great if you find your vassals have got there first...

Also, great when you capture some after a siege, esp. genius children which you can let stay rent-free in your dungeon until they reach 16 then work on making some geniuses of your own with their 'help'...
 
In my current game as the Fairhairs, Harald's wife never gave birth to a male heir, so I used my concubines to provide me with a boy. I couldn't get rid of my wife, so if it wasn't for my concubine, I'd be male heir-less. This is probably their most basic use. All the suggestions above are good uses too.
 
Concubines are supposed to help the ruler get more spawn.
 
Personally, I collect them. Gotta catch them all. At least one for each religion and culture. Not sure what the max is, but I'm going for them all.
 
If you take a child's mother, the enemy realm will still allow you educate the child with the mother. Who is now in your court. And you can sometimes demand her conversion.

Thus it can also be a way to stealth-convert realms, or at least destabilize them: kidnap the ruler's wife, concubine her, convert her to your religion, and then ask politely that the heir be educated with his mother. They will do it.
 
They also let you convert to a monotheistic religion, if you have one of that faith. Might be useful if you wanted to, e.g., become shia as a norwegian king.
 
well ... its not unheard of, of concubines teaching their 'husband' about their religion convincing him of the great things that happen if he convert to it :)

so as odd as it might sounds ... while implausible, its certainly not impossible
 
They're really useful as a Zoroastrian. Ensure your vassals are Zoroastrian, marry your sister/half-sister, and then get kids with a concubine. It's usually better to get a concubine first, then a related wife. That way your concubine children will inherit, and your marriage will get you loads of piety and prestige. Incest without the drawbacks! :p
 
This mechanic seems easy to exploit in many ways. I wonder if there will be a patch limiting this feature soon.

Doesn't that actually splits your demesne until you reform?...
 
well ... its not unheard of, of concubines teaching their 'husband' about their religion convincing him of the great things that happen if he convert to it :)

so as odd as it might sounds ... while implausible, its certainly not impossible

I don't know about concubines, but it happened quite frequently with wives. Clovis is the most famous example, but their Christian wives may have played at least some role in the conversions of Ethelberht of Kent and Edwin of Northumbria, for instance.