Invited to give a talk but could not attend, can it be on CV?
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.
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. For the same reason that you do not list the jobs that you declined on your CV.