Der Spiegel has an article on what it calls objectophilia, the phenomenon of quite literally falling in love with an inanimate object. It's purely anecdotal but for a conversation with a retired professor of sexology whose work I would need to be more familiar with before I granted his statements credit. Also, since it's a newspaper article written for a popular audience, the whole thing has an unfortunate "Look at the freaks!" quality, though it's not overbearing.
What I find interesting about the description of the article's subjects is that it really doesn't seem to be a primarily sexual relationship that they have with the objects of their affection. There is a sexual element which the article goes to some trouble to point out, but the people involved seem to have genuine love for their objects of choice, rather than a purely sexual lust. Mid-way through the article Joachim A. goes to some trouble to explain that what he and others have is not a fetish, and while he isn't very eloquent about it (in translation, at least), I think he's right.
The portions of the article that quote sexologist Volkmar Sigusch are a bit annoying. The quotes where he discusses asexuality and the increasing isolation of modern life make me think he sees it a primarily non-sexual, but then you have quotes about "Singles, isolated people, cultural sodomites, many perverts and sex addicts." I'm inclined to give Sigush the benefit of the doubt; I feel like the author of the piece may be taking the most salacious off-the-cuff statements from his interview with Sigusch and ripping them out of context to spice up the article.
I wonder, though, how much of this really is a modern development and how much is a long-standing but rare personality trait. I can't put my finger on any examples right now, but I recall having read in a lot of stories about people with strong, affectionate relationships with objects that they use daily. Doro B.'s discussion of the relationship she has with her metal processing machine strikes this chord particularly strongly. And, really, is having a strong emotional connection with your welding machine that much more bizarre than having a strong emotional connection with, for instance, your dog or your horse? I feel like the isolation of modern life might be a factor in drawing out the tendency to form bonds with inanimate objects, but I'm dubious that this is a new phenomenon.
Of course, what I don't know about psychology would fill the libraries of every psychology department at every university and institute in the world, so treat my thoughts on the subject accordingly. Nonetheless: Interesting article.