Much of the leveling in Diablo 3 is simply moving and the faster you move the faster you level. In addition it's very useful to be able to keep up in multiplayer. It rather sucks to find everything dead by the time you arrive over and over.
In addition to run speed when considering how fast you move consider Gold Pickup Radius. If you ignore gold then you don't especially have to worry about this affix in terms of your speed. But if, like me, you instinctively collect all the gold before moving on you will play through the game much quicker with some Gold Radius bonuses. I personally like at least 4 yards. This affix also boosts two Witch Doctor passives (Circle of Life and Grave Injustice). Note that the Demon Hunter can have a ferret companion that collects the gold for her.
Run speed is only found on boots in the Beta. The datamined affix information also says it can spawn on weapons and belts although that's probably a smaller amount and quite a high level. In addition legendary and set items get to break the normal rules. Run speed was quite a common set bonus in Diablo 2 and I'm sure that'll be true in D3 too.
The best mod in Beta that people can use is +7% although faster boots exist for unplayably high levels.
Faster movement is one of people's top priorities and most people will consider boots useless if they don't have faster movement. Even blue boots with one affix are reasonably expensive on the auction house but I doubt many players would buy rare boots with good affixes that lack movement speed. It's very noticeable, even a small percent.
Selling crafted faster boots should be a reasonably profitable niche market for people interested in that side of things.
As well as gear, each class has a greater or lesser degree of movement buffs from abilities runes and passives. Demon Hunters Barbarians and Monks all get good speed options, Wizards get Teleport and the poor Witch Doctor is a lot slower than everyone else.
These are the relevant abilities:
Leap . Covers distance quicker than running, allows otherwise impassable terrain to be navigated.
Frenzy - Vanguard. +15% move while Frenzying.
Sprint. +40% for 3 seconds, can be runed into Marathon (50% for 5 seconds) or Forced March (affects allies, 20% for 3 seconds). It looks like you can chain Sprints as long as you have the Fury.
Smoke Screen - Displacement gives +35% movement speed when activated (for 3 seconds presumably, the duration of the ability).
Shadow Power - Shadow Glide gives +40% for the 3 seconds it's active.
Tactical Advantage gives you +60% move for 2 seconds after you Vault, Smokescreen or flip with Evasive Fire. I've been using this in the Beta and it's really good. Monster packs aren't that far separated and a Vault or two is usually enough to get to the next pack.
Hot Pursuit gives you +15% when you're at Full Hatred. Another nice ability, best to open on packs with your spender and finish off the last few with your builder if you have this. Combines well perhaps with Vengeance because that fills you up after a fight, there's usually a few globes around after you kill a decent size group.
Way of the Hundred Fists - Blazing Fists applies a 5% move and attack speed buff every crit that stacks up to 3 times. Lasts 5 seconds.
Dashing Strike - Way of the Falling Star gives a +25% move speed buff for 3 seconds after you hit an enemy.
Mantra of Evasion - Wind through the Reeds adds a 5% move speed buff to the group.
Fleet Footed gives 10% movement speed. This is a very nice passive for so early on, arguably the best skill in the game.
Horrify - Stalker gives +20% for 4 seconds. The skill has a 20 second cooldown.
Spirit Walk seems to allow you to pass obstacles. Possibly it will let you walk through walls and doors which would be handy.
Spirit Vessel knocks 2 seconds off your Horrify and Spirit Walk cooldowns.
Teleport was really good in D2. The combination of moving very fast with ignoring walls made it the top movement skill in the game. In D3 it has a cooldown although the Wormhole rune seems to allow you to chain spam it. It may once again be the best skill in the game if you can feed it enough Arcane Power.
Archon has a rune just called Teleport that allows you to teleport when you're an Archon.
Illusionist is a passive that resets the cooldowns on Teleport and Mirror Image if you take 15% damage in a single hit.
In this area my beloved Witch Doctor class sucks royally. All of the others seem pretty good. I suspect that once people have good gear fast cast Wizards permaspamming Teleport will have the rest of us eating their dust.