Speed in Wurm Online is measured and expressed in kilometers per hour (km/h). Beside every player who can move at a speed, be slowed down or accelerated by certain conditions, there are vehicles and animals that move at various speeds that you can ride, like cows and horses on land, ships on water, or crocodiles that can do both. Yes, you can tame, or as a priest of Libila, re-animate crocodiles and ride them on land and water.
Walking or running
You can not run in Wurm like in other games, where you can perhaps toggle between walking and running, or even temporarily sprint at an even faster pace. Your walking speed is affected by the weight you're carrying, any armour and clothing you're wearing, any player status effects you might have, the slope you're walking up or down, and largely the type of map tile you're walking on.
Your speed can be anywhere between 4.90 km/h on tar to 17.3 km/h on cobblestone when not encumbered and on a flat surface. Walking consumes your stamina at various rates, depending on many things mentioned above. If you run out of stamina, you will be exhausted and greatly slowed down.
Travelling on roads and highways is one of the fastest ways to get around. They usually have pavement that allows you to walk at the highest speeds. Established servers more often than not, have a well developed road infrastructure entirely built by players. If you find a place to settle in a speck of wilderness, you will have to build your own roads.
Your base swimming speed is about 8.20 km/h when unencumbered, but can be slowed down by mostly the same things as walking. It does consume stamina, and you can not regenerate stamina naturally while swimming. If you run out of stamina and continue moving, you will start drowning and accumulate water wound damage until you die.
When climbing, your walking speed is greatly slowed down to at least 4.30 km/h on flat rock tiles or pavement. Climbing consumes a lot of stamina on steep stopes, and you can not regenerate stamina naturally. If you continue climbing when running out of stamina, you will be forced out of the climbing mode sooner or later, depending on your climbing skill.
While mounts are technically vehicles, they're commonly rather referred to as a living creatures that can age and die, be killed in combat, and move at slower speeds when hungry, instead of a mechanical vehicle.
There are a number of animals and monsters you can ride as mounts if you meet the requirements. Once tamed or dominated, some can wear animal equipment that can make them move and turn considerably faster. They are not affected by tile types and pavement, and move at their regular speed, even on tar.
Mounts ignore the amount of stamina you have, and won't slow down if their rider is exhausted. You will not regenerate stamina while riding when standing on a steep slope. They are however affected by slopes you're riding up or down. Mounts can walk up and down slopes of up to 40 dirts.
Some bred animals with speed traits and good animal equipment can reach speeds in excess of 30 km/h on any terrain. Others, while still useful for dragging carts, are only able to move at speeds slower than a walking player. But you're not riding your scorpion through town because you want to go fast, do you?
Only unicorns and crocodiles allow passengers when ridden.
Vehicles, with the exception of the wagon and ship transporter, can take 2 to 13 passengers, in addition to the driver. A wagon can carry 1 additional passenger. To control a vehicle, you will have to embark it as commander, it's generally referred to as to sail a boat or to drive a cart. Passengers have to embark as passenger. They are controlled by the player's movement keys, sped up by walking forward, slowed down or backed up by walking backwards, and turned by strafing left or right. Vehicles can drive up and down slopes of up to 40. Driving vehicles consumes stamina, and you can not regenerate stamina while standing on a steep slope. However vehicles do not slow down when you run out of stamina.
Ship transporters are by far the slowest vehicle you can drive, it can be dragged by a player, or by up to 2 animals, and they can not seat any passengers.
While their speeds are not very high, and often slower than a walking player, their ability to transport large amounts of items and heavy loads makes them very useful. Bred horses with speed traits and good equipment though, can drag your sports cart at over 20 km/h.
Rafts, although able to float on water, can not be embarked and used as a vessel. They can only be dragged by players like a small cart.
Boats and ships
Rowboats can drift slightly in the wind, but are mainly propelled by walking as the commander. They're overall the slowest vessel to use. Sailboats make much more use of wind while not largely dependent on it, but like bigger ships still make use of the commander's walking. Larger ships are highly dependent on wind, and can reach speeds in excess of 30 km/h in a gale, but can still receive a small boost from the commander.
Every passenger will passively speed up the boat or ship a little, helping to reach its maximum speed.