I have a friend in California, and if I understood him correctly, the taxes in California reward patience, i.e., they stay the same based on the purchase price based on the period of time you live in the house! Others have answered the bulk of the questions here, but just remember in MA, the taxes change every year. Oh, and by change, I mean "go up", although I'm sure there are a few exceptions to that. Fortunately, this system does moderate the increases somewhat.
What the tax rate (percentage of assessed value) is does in fact get set each year by the local municipal government. But it is not as arbitrary as it seems. The officials are restricted by proposition 2 1/2. However, it may still seem arbitrary to many people.
Details on Prop 2 1/2
The factor of 2 1/2 % comes into play in two ways.
1. It's a ceiling A city or town may only collect, AT MOST, the equivalent of 2.5% of the taxable property value in the city or town. For instance, a town that has real property value of approximately 6,000,000,000 can only collect a MAXIMUM of $150,000,000 in taxes.
2. It's a cap on increase. A city or town may only INCREASE it's taxable income by 2.5% of the taxable properties minus new growth. Tax on new growth is all increase to the tax base. So, if that same town that can not collect ore than $150,000,000 in taxes .. ran on $100,000,000 dollars, may only collect $102,500,000 the next year + new growth. The burden of that $102,500,000 of taxes is then divided proportionally across all the taxable properties in the city (given one rate for Residential and another for Business). Residential properties are assessed based on "market price" of two years prior. Business properties are assessed based on their revenues and then taxed (often at a higher rate than residential tax).