I have thoughts about A Scandal in Belgravia, and they have nothing to do with the is it or isn't it sexist argument that everyone is having. I'll leave that to everyone else; I have thoughts about Mycroft to discuss.
As you can see in this picture, he's wearing a wedding band. However, we never see or hear mention of a wife or partner. Below, my thoughts on why the ring might be there.
1. Mycroft is married to someone with an equally time-consuming job.
I think this is probably the least likely explanation, for a few reasons. First, I feel like we would have heard her at least mentioned if not seen. More importantly, though, Mycroft setting Sherlock and himself apart from other people when he says that "caring is not an advantage" makes no sense if he does, in fact, currently have a spouse in his life who he (presumably) cares for.
2. Mycroft is divorced.
If this is the case, "caring is not an advantage" takes on an interesting ring in context- bitter, probably, knowledge that Mycroft has gotten from personal experience. Mycroft has been burned before- maybe he's trying to protect Sherlock from going through that himself. Maybe he got divorced because he felt it compromised his logic. The fact that he keeps the ring and wears it could suggest he has regrets about what happened; it could also be Mycroft's reminder to himself not to make the same mistake twice.
3. Mycroft is a widower.
"All lives end," Mycroft says, "all hearts are broken." Given that quote, I think this is the one I personally think is most likely. Possibly his spouse even died as a result of Mycroft's work, was somehow caught in the crossfire or used as leverage against him. I like this interpretation because I suspect Mycroft of not always having been as collected and impersonal as we see him now, and a tragedy like that would certainly be a viable explanation for his character's coldness.
4. Mycroft is not, and has never been, married.
Mycroft is resolutely single and refuses to get emotionally involved with anyone, but wears a wedding ring to discorage people and seem normal and well-adjusted. Mycroft, unlike Sherlock, pays enough attention to how society works that he can function within it; it could just be a misdirect.