Not at the state level; I'm not aware of any state that does. But I assume Tennessee's state constitution permit counties and municipalities typically levy these taxes, which, of course, they do. They vary so much from county to county and city to city, both in nominal rate and in appraisal practices, that interstate comparisons are almost impossible.
I don't like taxes any more than the next FReeper, but property taxes -- taxes merely on having something as opposed to taxes on earnings or spending -- are particularly odious.
I actually believe in sales tax.
On the other hand, a local tax on property could be justified by the services that are received by that property... access by maintained county roads, police, fire, schools servicing the area... I'm not pro-tax or pro-property tax, but it seems at least as reasonable as a tax on income. I'll grant you the issue with the taxes increasing over time.
And I can honestly say that I am more tolerant of taxes at the local level than at a greater distance (federal, for example), since county taxes get spent in the county (or city).