If I was invited to give a talk but was not able to attend, could it be listed under invited talks in a CV? My point is that there was an invitation and it worth to show it. Similarly, a paper can be accepted for a conference and no one of the authors presented it but it was published in the proceedings. Or a someone receive an award as a sign of recognition.
An invited talk is not about being invited but more about giving a talk.
Strictly speaking, there is nothing that you did: You have not given the talk, thus, I would not include it into the CV.
Regarding your comparison with papers that were not presented: The main contribution of a paper is the result which is included in the proceedings. Presenting a paper is just an extension and explanation of your results. So the majority of the novelty and effort went into the paper itself. Please note that there are also journal papers which are (mostly) not presented at all. The same is true for conference papers which I include in my CV despite I have not presented them myself, because on of the co-authors did it.
No: Don't list anything that you didn't do.
From a comment on my answer:
He's not saying he'll pretend he gave the talk. The invitation itself is a good indicator of his status as an expert in the relevant field, at least in the eyes of the people running the conference. If this is relevant to the job, I don't see a reason not to include it, as long as he makes it clear he didn't give the talk.
which was extended to add:
If Google or Apple offered me a job, but I couldn't relocate or whatever, I'd absolutely put it on my CV.
A comment on another answer provides an excellent response:
if I saw such a claim on your CV I wouldn't even invite you to an interview. If you didn't take the job, if you didn't go to the presentation, if you didn't do the thing, it doesn't count. It never happened; it doesn't count.
Another commenter writes:
It may be a accomplishment, but it is also a opportunity wasted. You do not really want to underline your failures to execute. Its a bit like saying businessman saying they got a big contract but never fulfilled it. People are looking for people who can get things done.
I don't understand the other answers. Being invited to give a talk at a conference is an indicator of esteem, regardless of whether you could make it. I see no harm in writing
Great Conference (2017), invited to give plenary talk on topic X, but could not attend.
Mentioning in CVs declined jobs, grants and scholarship and funding is common in some fields, see e.g. the results of this search, http://www.google.com/search?q=high+energy+physics+cv+declined
In fact, one of the first hits mentions at least half a dozen declined declined talks
Being invited does certainly count for something. However, if you were unable to attend, for whatever reasons, then you shouldn't put it on your CV.
It wasn't important enough to me at the time, but I am adding it to my CV because I think it could impress someone...
Having said that... if you actually wrote the paper (or, co-wrote) that prompted the invitation, then you should definitely add that to your CV, because the writing is an achievement.
Despite everyone saying 'no', I'm pretty sure yes, you can. Is that a good idea? Most likely not.
Unless that talk is really prestigious and invitation to it underlines an important accomplishment and you had a good reason not to attend, like sickness or no means to make a trip AND you have nothing better to put on your CV AND you can specify that you were invited, did not attend, because of (a good reason) without writing an essay on your CV, AND you make it valuable to your potential employer and not look like an exercise in vanity, AND... well, you get the point