Having built wooden bows up to 80lbs myself and taken part in reenactment, i can say: it depends on the wood, the bow's construction, the string and the arrow (besides weather, geography/topography, wind and the archer, of course).
Without helping gear for aiming or visual references, a good traditional archer can maintain a narrow distribution disk up to ~20-30m when shooting level on a range with an equal flight of arrows, considerably less when shooting in nature with its ups and downs, obstructions and distractions. Traditional bow hunting is stalking, on a less degree with fully equipped modern compound bows and fiber arrows.
Long range shots, e.g. clout shooting, are mass shootings. A quick archer can keep 2-3 arrows flying, and 50 archers will produce a nice optical and acoustical coulisse :-). The arrows are shot at ~45°, when they impact they only have their respective terminal velocity. But if the head is a long needle, it'll still poke through a light armour or ring mail or a skull's orbit.
Long shots in traditional archery, level and without wind, are around 200-250m meters, as others have noted. My longest one was ~180m with a 65lbs Osage Orange bow, arrow with natural feathers and forged head, wayfarer shaft. It would have been a little more with a much lighter fibre glass arrow.
As to the range of the longbows, chronicles of the Battle of Agincourt that was already mentioned here say that the arrows were feared of piercing light armour at the joints up to distance of 220 to 200 yards, though these were of course unaimed ballistic shots. I would see that range as the maximum effective range under these conditions, farther would mostly be a waste of arrows, imo.
Also mentioned is the wreck of the Mary Rose, that contained a load of staves and bows. Though some technical data (especially the draw weight) is still discussed, we can assume a draw weight of 100 to 160lbs. Quite a few replicas have been made.
Traditional Bowyer's Bible, Volumes 1 to 4.