At closing, does the buyer or seller typically pay the property taxes?
In my area, the taxes are typically pro-rated to the date of closing - that is, the seller pays the days that he or she owned the house, and the buyer pays any remaining days in the current bill - as well as any bill that is due within 60 days of the closing. (Because there is a delay before a buyer's first payment is due, the money for the upcoming bill is collected at the closing tro be certain that it is paid on time).
In some areas, this practice may be different - and there may be more taxes than "property" - there may be county, school, or other taxes as well. All taxes may be negotiated as part of the purchase agreement - if the seller's agreement to pay the upcoming tax bill is enough to make a price agreeable to both parties, there is nothing stopping the parties from making this agreement - BEFORE a purchase contract is signed.
At closing the property taxes are pro-rated according to usage of the property. That is, the seller's responsibility is to pay taxes accrued to the date of closing, while the purchaser's responsibility is moving forward. How this is handled at closing usually requires a credit to the purchaser from the seller.
For example, in many Virginia counties and cities, the due date is June 5 for 1st half taxes and December 5 for 2nd half taxes. A closing at the end of July would require the seller to pay a month's worth of accrued, not not yet paid taxes to the purchaser as a credit on the HUD1 settlement statement.
The purchaser's requirement is to establish a large enough escrow account with the lender to be able to pay future tax bills, regardless of when they actually bought the house. So, while a purchaser may have to establish an escrow account of up to 8 months of taxes and the federal guidelines allow a 2 month cushion at the highest point in the next 12 months, much of that 8 months will be credited back to them at closing by the seller.