This is the law in Utah and was applied to all businesses up until a few years ago. I don't think they ever tried to property tax the personal possessions of individuals, though that was the law.
You were required to declare your chairs and desks and tables, calculators, paper and pens, books, bicycles, cameras and computers, and everything and look up its market value and then pay the usual tax just as if it were real estate. You were required to do it every single year. And it's still the law for property above an exempt amount, but no longer applies to every paperclip like it used to.
That law is crazy, of course. Real estate is a big expensive immovable item that creates limits on the level of corruption and record keeping headaches so it's the best target for property taxation. Maybe really big vehicles like cars and airplanes and boats could be targets, too, if they have a home base, but even then you can see problems.
And finally, Henry George [0] points out that the ideal property tax to promote investment, limit corruption and cheating, allow fair administration, limit any kind of dead-weight loss [1], and generate reasonable revenue would be a tax on land value only. Buildings, improvements, vehicles, and personal property should be exempt and only the land's location, area, and fixed geology/hydrology/soil conditions should matter.
[0] http://en.wikipedia.org/wiki/Georgism
[1] http://en.wikipedia.org/wiki/Excess_burden_of_taxation