Not exactly. Barbarians have "Sprint" which directly affects their run speed, allowing them to run out of a difficult fight =)
I suppose I could be a bit more clear, but the point remains the same. Spirit walk, Teleport, Leap Attack, they can all get you from A to B faster than walking/running would normally allow. They all also have cool downs and quite probably hefty resource requirements.
More specifically, you can't just teleport through the game now, run past all the mobs, or sprint through to areas you like more. You also can't town portal out of situations just because things are tough anymore.
That being said, movement speed modifiers (That always affect it, or at least for prolonged periods of time) are removed from the game and for good reason. It upsets the balance of the game.
As to the other comments on my post. If it is a negligible difference in speed (1-5%) then there's no real draw back to going heavy armor. Which pretty much puts us back at square one. If you can't really tell the difference then you're not really trading anything off. Everyone would simply use heavy armor end of story.
If you kick it up to anything much higher that is noticeable people will be disinclined to play the "slow build." Whether or not they notice it players who are significantly slowed by armor will in fact level slower (that's pretty simple math.) With tank builds not being a requirement as in wow they won't be as viable by comparison. Additionally with it already well established that items won't have +movement speed modifiers (if you don't think so go dig around on it) it will ultimately be an unattractive and terrible function to the game. If it were slow enough (Upwards of 15% - 40%) people would simply play other classes that are faster to get gear before ever attempting to get a "Defensive build." And then we come full circle, D2 all over again, where people make fast killers to mf and get gear, and using the gear dependent classes as their final product once they have the gear.
This isn't Diablo 2, get over it, move on, and accept the fact that they're actually going to improve the functionality. If you want to have a penalty for wearing heavy armor, by all means, slow yourself down. The rest of the player base doesn't want to be held back without just cause.
The slanted eyes, so unearthly a gray color that they seized the attention of all who looked into them. Yet almost immediately those same eyes repelled, for in them Kentril sensed his own mortality.