With most US-based frequent flyer programs, what you see is what you get when it comes to award tickets. If you're booking a Business Class ticket from New York to Rome that costs 100,000 miles roundtrip, you'll pay that amount, along with nominal taxes and fees. For programs and airlines based in other countries, however, significant co-pays are the norm, meaning that award ticket could come along with hundreds of dollars in fees -- airlines often refer to these fees as a "fuel surcharge," though they generally have little to do with the cost of fuel.
Initially, fuel surcharges were created so airlines could adjust prices on the fly in response to fluctuating fuel costs, without boosting the base fares. Now, these surcharges are used to inflate the fares beyond the base ticket amount, with little to no relation to the price of fuel. For example, an airline may charge $300 for a roundtrip Coach fare between Chicago and London, but the total price you'll pay for the ticket could be $800 or more. In this scenario, the airline is tacking on a fuel surcharge of at least $400, along with other miscellaneous taxes and fees. Generally, you won't ever notice this charge when booking a paid ticket, but it could pop up as a nasty surprise when it comes time to secure an award seat.
Certain international carriers, such as British Airways and Singapore Airlines, add fuel surcharges to most awards, including regional flights. Most often, you'll avoid paying these on flights that begin and end in the US (if you're using British Airways Avios to fly on American, for example, or Singapore miles to fly United), but if the flight brings you from one country to another, you could be on the hook for very significant surcharges, that increase as you move up to a higher class of service.
Many times, fuel surcharges make an award redemption illogical, unless you're redeeming for Business or First Class. With that $300 Coach fare above, for example, the miles will only offset that base rate, but not the $400 in fuel surcharges and $100 in taxes. You may be expected to pay fuel surcharges when using US-based miles for travel on an international carrier, too.
You can use American's AAdvantage program to book British Airways flights, for example, but you'll have to pay the same fuel surcharges you would with BA's own program, making the flight quite a bit pricier than if you were flying on an AA aircraft.
Regardless of whether or not you have to pay fuel surcharges, you're always on the hook for tax. For domestic flights in the US, taxes are usually limited to a $2.50 per-segment September 11th security fee, which covers the cost of TSA screening (yes, you're paying for that pat down). When you add international segments to an itinerary, however, the taxes really start to pile up. Some countries charge significant departure taxes, that can sometimes run into the hundreds of dollars, such as when departing a UK airport on an overseas flight.
All countries charge a tax of some sort, which you'll be responsible for paying one way or another. Most of the time, the amount is factored into the price of a ticket or paired with a mileage award, but some countries require that you pay the tax in cash before you check in for your flight, so keep in mind that even if you don't see taxes tacked on to an award, you could still be on the hook for a small amount.
Fuel surcharges are always charged in advance, however -- if they don't appear when you're booking, you should be in the clear.