If you're talking about something that is physically part of the bookcase (like glass doors), then you'd say 'on' - eg. there are some nice glass doors on my bookcase. If you're talking about items that can be removed from it (ie, books) then you'd say 'in'. eg. there are lots of books in my bookcase. Julia is right about bookshelf, as it's something you put things on top of - you'd say 'on the bookshelf'.

Yes, they are both right. If something is "on the bookcase" it is on top of the bookcase. If something is "in the bookcase" then that something has been placed in one of the shelves of the bookcase.

I think technically, you would use "on the book case" when an object is "on top of" the book case; and you would use "in the bookcase" when it's on one of the shelves within the bookcase. However, I think many people say "on the bookcase" when they mean "in the bookcase". If you had a bookshelf that is just a single shelf — then I think "on the bookshelf" makes more sense — it's on the top-most part of the object.

Miss Helen, I think it is not so important whether "other people who ..."are wrong. It is more important to think, "If I wish to follow best practice, what.should I say or write?" Here are my recommended answers: 1. Please leave these books on the bookshelves. 2. I am think of putting some really big blue and white vases on top of the bookcase. That would be gery chic. 3. There is nothing in the bookcase. 4. The cigar cutter is in the drawer at the bookcase.