If I prepay next year's taxes this year, can I deduct them this year?
Probably. Generally speaking, taxes are deductible in the year you pay them.
Sometimes real estate taxes are prepaid. If you are the property owner, you can generally deduct prepaid real estate taxes in the year of the prepayment if (1) you are a cash basis taxpayer and (2) you don't live in a jurisdiction where the taxing authority considers prepayment a "deposit." Jurisdictions vary regarding how they treat prepaid tax. Be aware that taxes placed in escrow generally aren't deductible until they are paid to the taxing authority.