I have a bunch of physical books, and I would like to have ebook versions of some of them. It doesn't seem like I should have to pay the full ebook price. I know about Matchbook, but these aren't books I bought from Amazon. Do any publishers give deals on their ebooks if you've previously bought the real book from them (don't know how you would prove it though)?
This would depend on the publisher, and as you mention, it's difficult to prove that you bought the book unless you bought it directly from the publisher and they have a record of it. Many publishers will offer discounts if you're buying both the ebook version and the print version, so it doesn't hurt to ask if you've bought directly from a publisher, but if it's from a retailer it's less likely.
There's a new service called Shelfie.com which does exactly what you say. It's a little convoluted. You have to photograph your bookshelf with your phone, and it will offer reduced price on the ebook. The proof of book ownership takes the form of signing your title page and uploading a picture of the book title's page.
There are 3 problems with the service. You can only read the ebook on a special ebook reader, only 1/10 of the ebooks are eligible for this service (and that's being optimistic). But it could gain momentum.