At your company, action items are recorded during meetings and people are held responsible for carrying them out or Not?

Definitely they are held responsible for the action items, discussed in agreed upon in a meeting. The meeting minutes which are being circulated after the meeting, highlights these points, and all the concerned who have been given the responsibility to take action are later on held responsible.

Yes.

One of the most important aspects of holding a meeting is to agree on tasks that should be carried out. As soon as possible post-meeting, distribute a report and list of action items to each participant. Each item should have a clear expectation of what is necessary for successful completion, as well as a due date.