All Avalon and Camry engines utilize a timing belt to drive the camshaft from the crankshaft's turning motion and to maintain proper valve timing. Some manufacturer's schedule periodic timing belt replacement to assure optimum engine performance, to make sure the motorist is never stranded should the belt break (as the engine will stop instantly) and for some (manufacturer's with interference motors) to prevent the possibility of severe internal engine damage should the belt break.
Although these engines are not listed as interference motors (it is not listed by the manufacturer as a motor whose valves might contact the pistons if the camshaft was rotated separately from the crankshaft) the first 2 reasons for periodic replacement still apply. Toyota does recommend replacement for these motors at 60,000 miles (96,000 km) if your vehicle is driven under conditions of extensive idling or low speed driving for a long distance such as a police car, taxi or door-to-door delivery usage. You will have to decide for yourself if the peace of mind offered by a new belt is worth it on higher mileage engines.
Whether or not you decide to replace it, you would be wise to check it periodically to make sure it has not become damaged or worn. Generally speaking, a severely damaged belt will show as engine performance would drop dramatically, but a damaged belt (which could give out suddenly) may not give as much warning. In general, any time the engine timing cover(s) is(are) removed you should inspect the belt for premature parting, severe cracks or missing teeth.