There's a minor industry devoted to customized imagery and colors for consumer product. There are startups set up to serve that market, with online design tools.[1][2]. Custom shoes and sports equipment are doing reasonably well. The T-shirt industry has been doing this for at least half a century. Bain, the consulting firm, has an article on what works in product customization.[3] Basically, let the user tweak minor stuff, but not change much.
None of these companies actually let the user affect product function much. It's all decorative, or sizing-related. Autodesk has gone further, with Autodesk Homestyler, which is a free CAD system for home interiors.[4] This is a descendant of Autodesk Kitchen Designer, which was for sizing kitchen cabinets to fit a kitchen space. This lets you lay out a house, existing or planned, add commercial furniture, and view the house in 3D. Available for desktop, browser, and mobile. Despite being an impressive tool, it's never caught on. Probably because most people are terrified of starting with a blank screen and designing their house.
Carl Bass, the CEO of Autodesk, thinks that user design mods and product customization will be important, but aren't here yet. Autodesk has come out with a range of low-end CAD products. They now have their own 3D printer, and there are things like their 123Catch, for turning sets of pictures into 3D models. The technology is doing fine. But designing your own stuff isn't an instant-gratification thing.
[1] http://www.dogma.com
[2] http://www.fluid.com
[3] http://www.bain.com/publications/articles/making-it-personal...
[4] http://www.homestyler.com/floorplan/