How are my property taxes calculated?

There are two components to real estate property taxes: the assessed value and the assigned rate. Both are set by the County and change every year. So assessed value * tax rate = property tax bill. So even if your assessed values go down, your tax bill could go up if the tax rate changes enough! After all, the government still needs their money to keep things running.

You can see easily look up assessed values by property address:
Fairfax County
Arlington County
Alexandria City
District of Columbia

Tax rates vary by jurisdiction, of course. Rates for 2009:
Fairfax County $1.05 (per $1000 in assessed value)
Arlington $0.865
Alexandria City $0.903
DC $0.85 but beware of vacant properties -- it jumps to $10!

You should note that a tax assessment is very different than an appraisal, and both of those values may be different than the price you paid for the home even this year! Assessments are generally adjusted every year (depending on the jurisdiction), and looks at all sales in a 12 month period. Most assessments do take into account the market value, but do not mirror it exactly. Fairfax County's website, for example, says "Given the size, complexity and diversity of properties within Fairfax County, fair market value is deemed to be reasonably estimated if assessments at the neighborhood level generally average in the low 90's percent range when compared to sales prices." So in other words, if the tax assessed value is approximately 90-95% of the estimated sales price, it's considered to be the fair market value for tax purposes.

Here is a helpful faq on Fairfax Co property taxes,

and here is one for Arlington County.

You always have the right to appeal your property tax assessed values, but the timing and process vary by jurisdiction.

Tax bills can also be affected by deductions or exemptions. The District, for example, has the Homestead Deduction for owner-occupied properties, which reduces your tax bill by deducting $67,500 from your assessed value. There are several other programs, so home buyers do your research -- and most importantly, do NOT assume that the prior owner's tax bill will be your own total due. One of the most important exemptions is the Assessment Cap Credit, which provides that an owner can not be taxed on more than a 10% increase in the assessed value. What this means in practice is this: If you are buying a property from a long-term owner, chances are their tax bill is significantly lower than the one you will have as a new buyer not subject to that cap. Budget carefully!

Because assessed values are only updated every 1-3 years, often the assessed value might be HIGHER than the current market value. Here's a good article in the Washington Post describing how to appeal your assessment.