The prevailing wisdom has been to separate your animations from your movement. I.e. Animate the character in-place and move it via code. Dependent on your game type, this can indeed be the better method.
However, Unity (4.x) provides the Mecanim animation system, which allows for root motion to be applied from the animation to the character's in-game transform. In order for root motion from the animation to be applied, make sure the "Apply Root Motion" option is checked in the animator component.
Mecanim will also retarget animations for humanoid rigs auto-magically. By using the retargeting with root motion, you can use the same animations for a long-legged character and a short-legged character, and the movement will then (auto-magically) line up with the animation.
Skeletal meshes should include an animator component by default as of Unity 4.3, and I believe this is still the case as of 4.3.4.
Using Mecanim will also require you to make an Animator Controller, which is a state machine for controlling your animations.
The Mecanim reference can be found in the Unity manual pages here.