It is normally not a fixed percentage of your value, but simply "here's what the county/city paid this/next year, divided amongst the properties proportionate to the value."
Some, like sewer, etc, are per-property, but most are done via the above.
California is an outlier because of Prop-13 but that makes it usually better except when buying.
Side-effects of this can mean that development in your district can reduce your tax rate, depending on what kind of development and who lives there (as property tax is often mainly a school tax, a development for 55+ will bring in more tax payers but not increase the school burden noticeably).
Like with any tax, I'm guessing the rate would change if the county's revenues didn't match their expenses?
My property taxes have practically only gone up over the years, but the tax rates from the various entities have mostly trended downwards.