I'm trying to collect this information in one place so it's easy for me to find. I thought I'd put it on my blog so others can also use it.
Conestoga Wagons were drawn by 4 to 8 horses and transported loads up to 7 metric tons. They averaged 15 miles a day (usually over dirt roads).
Wagon Trains averaged 12 to 16 miles a day.
Two-wheeled loaded carts pulled by two horses could travel at 5 miles per hour if the horses were switched with fresh ones once or twice each day. If the same horses were used all day every day, the wagon could travel at 4 miles per hour.
A lone traveler on foot carrying very little can walk at about 3 or 4 miles per hour. How long he can keep it up depends on his endurance. A marathon runner can do 8 miles per hour but likely couldn't keep that up day after day.
A very fit person trained for travelling over mountain trails or through the desert can, with a heavy pack (containing food and supplies),
at best do about 20 miles in one day. Without a pack, he can make about 30 miles if he hikes fast all day. An experienced hiker not trying for a record does about 2 to 3 miles per hour.
A messenger pigeon can travel 30 miles per hour normally and 60 miles per hour in a burst.
Foot soldiers averaged a pace of 3 miles per hour. The soldiers could do this carrying fairly heavy loads (their equipment and some rations). Rain and muddy roads could cut this travel rate in half (to about 1.5 miles per hour). Forced marches usually meant marching longer (which left the soldiers exhausted at the end) rather than faster.
An army has to take time each day to break camp, load tents and such into wagons, and then set up camp at the end of the march--all of which cuts into how far they can travel in a day. The larger the army, the slower it moved. The Romans, who built temporary forts every night, often travelled only 10 to 12 miles a day even when travelling along their stone roads. Smaller armies that made less-fortified camps might be able to do 16 to 22 miles a day, but that was considered a hard pace.
The cavalry could travel faster, but they generally kept to the pace of the foot soldiers or were sent ahead to the next camp site since they had to graze their horses on good grass for about 5 hours every day. The Roman cavalry, when on its own, could do 40 miles a day.
A less-organized army might average 8 miles per day for the infantry and 12 miles per day for the cavalry.
An average horse bearing an average rider with minimal equipment along a road or good, fairly flat trail can travel 3 to 4 miles per hour at a walk, 8 to 10 miles per hour at a trot, 10 to 17 miles per hour at a canter, and up to 30 miles per hour at a gallop. A horse can not keep up a canter or gallop for more than a few miles, though. Exceptional thoroughbreds can go over 40 miles per hour for a mile. Quarter horses can reach up to 50 miles per hour for a quarter of a mile. Rough terrain would slow all these rates.
How far a horse and rider could travel in a day depends on the time of year, weather, terrain, condition of the roads, load carried (rider and equipment), and condition of the horse. A fit riding horse ridden by a fantasy warrior might cover 50 to 60 miles in a day, but 30 miles would be more average. A fantasy farm boy riding an old plow horse would go even slower than that.
An endurance horse bearing a light rider with very minimal equipment can travel 100 miles in a day on a trail over rough terrain. The horse would need several short breaks (15 to 30 minutes) to rest during the ride and couldn't repeat the performance the next day. The horse mainly travels at a trot, with some walking (up hills) and some cantering (on flat areas). Keep in mind that these horses are highly fit horses specially trained for these distances. They are well-fed, healthy, and have plenty of water available. Take away any of these factors, and the horse can't travel as far.
The Pony Express was made up of smaller horses and ponies who carried 165 pounds (including rider, mail, and supplies/equipment). Ponies were changed for fresh ones every 10 to 15 miles, and riders were changed for fresh ones every 75–100 miles. The horses traveled at about 10 miles per hour, and the mail was moved an average of 250 miles in a 24-hour day. The trail was mostly one of dirt.
Riding camels can travel over 100 miles in a day. Racing camels travel an average of 20 miles per hour during 6-miles races. A camel can travel 60 miles a day across the desert carrying up to 400 pounds. Camels can carry as much as 600 pounds if loaded properly.