Playing a loyal Saxon of Surrey. Would it be appropriate to take a Concubine? How many can one take? Is there glory for having many, or penalties for having few? Does Arthur ever prevent the practice?

Depends on your GM, but the way I would be GMing it...

1) Any children by a concubine would be an acknowledged bastard, not a legitimate child. Hence, if your liege is a Christian, they would not accept your bastards as your heirs. If your liege is a Pagan or a Wotanist, he might be fine with your concubines and your bastards, but that might lead to an argument with any legitimate branches (either your own legitimate children or your siblings, who would claim the right to inherit over the bastards).

2) Your legitimate wife would no doubt dislike you having a concubine, let alone several. (Unless she hates your guts already and is relieved to have as little to do with you as possible.) Her family might object, too.

3) Lustful checks, of course.

4) Support for concubines and acknowledged bastards: £1 for the concubine + £1 if there are any children. Stopping the support would give Selfish checks and lower Love (Family), although marrying her off to a knight who can keep her and the children up in similar style would be acceptable. (Common-born mistresses and unacknowledged bastards can be handed off to (wealthy) commoners, and cost only half to maintain, too.)


So to answer your exact questions:
A) Appropriate? No, not really. The society as the whole is Christian, so you are better off marrying. If you are unmarried and want to keep your options open, then sure, go for it.
B) How many? In principle, as many as you can support (see 4. above). But they might resent becoming a harem (see 2. above). Easier if you can install them in separate manors, preferably far apart.
C) Glory? Nope.
D) Arthur? I don't think he would stop it, but he would support the rights of the legitimate wife and children. He might also refuse to accord any official status to the concubine. She is a mistress, pure and simple, so do not bring her to court to cause offense to the good and pure damsels of the court (we won't speak of what those damsels might get up to with the Courtly Amour).

Morien sums it up quit nicely and I would probably GM it the same way.

One addition:
The practice will have effect on three families:
1) Your own. Heritage will get interesting, as Morien mentioned, but it may also tarnish the reputation of the family (or enhance it. Being a Saxon after all). Would you marry of your daughter/sister to such a man, knowing that he will probably make life hard for her and her children? And if this knight is like this, how about the rest of his family?
2) The family of your legitimate wife. They will probably not be pleased with such an arrangement. Especially if there are bastard children in the mix.
3) The family of the concubine. The family may think that they can get some kind of power from the relation, even if it is not official, but the girl is spoiled goods. Marrying her to other strong families may be difficult.

So it could open a can of snakes and may bite you in the end. Of course all those intrigue will give you some glory as you try to manouver through all the machinations, but other than that I would not give any glory.

3) The family of the concubine. The family may think that they can get some kind of power from the relation, even if it is not official, but the girl is spoiled goods. Marrying her to other strong families may be difficult.

Yes, there is almost certainly a stark power differential between the families here. No equal or even semi-equal family would consider a concubinage good enough for their daughter. So you are really looking more like making an alliance with someone much weaker than you (the concubinage family), and very likely pissing off an equal family (of your wife, if any).

For a knight, the concubinage family would be commoners, most likely, as no noble family would consent to such an arrangement.

For an estate holder, I could see some esquire family deciding that something is better than nothing, to get a son knighted and/or other sons appointed to offices within the household, etc.

For a baron, a knightly family starts to become possible.

A king might even go after a baronial lady. It is good to be the king. You might notice that Uther tends to dally with commoners, though. Much easier, much less of a hassle, much less expensive! After all, dealing with a noble girl tends to involve elevating her noble relations as well, and this tends to make the other noble families jealous and resentful, as one family is honored due to their services in the king's bedroom. For example, the Boleyns (of Henry VIII fame).

Although to note that since the (Roman) Church doesn't approve of the concubinage, those women would be 'just' mistresses, without an official sanction. Although everyone knows. Historically, having such mistresses was very common for kings especially, since who would tell them no? Henry I had about two dozen acknowledged bastards, and who knows how many more unacknowledged ones? Ironically, no legitimate sons, leading to the Anarchy...

And just out of curiosity, what happens if the concubine is a high noble who has a title and the wife does not?

Thinking of role-playing possibilities here. One of my older characters did end up marrying a princess, and did not dally with the other lass, but it could have been different...

And just out of curiosity, what happens if the concubine is a high noble who has a title and the wife does not?

Almost certainly will not happen. Why would the high noble accept being a concubine, a title that is just a step above that of a prostitute, ruining her reputation? I mean, she would be smarter to just be a lover and keep things under wraps.

If the concubinage is a potential option, that implies that the culture is more permissive of things like polygamy and divorce. For instance, medieval Welsh law allowed the woman to divorce her husband if she caught him cheating on her three times. So it might be possible for the husband to divorce the commoner wife and then marry the high noble.

For really desperate ones, there is always the foul means: framing the wife for adultery or just arranging for an 'accident'.

To sum it all up:
Getting married is a political move. Taking on concubines or mistresses is a political move. Both may result in trouble for yourself, your family and your children.
So you need to be careful who you marry and who you take on as your lover.
Unfortunately not getting married is also trouble in the future for your family. so it is a catch22.