The power of a Nord can be articulated into a shout, like the kiai of an Akaviri swordsman. The strongest of their warriors are called "Tongues." When the Nords attack a city, they take no siege engines or cavalry; the Tongues form in a wedge in front of the gatehouse, and draw in breath. When the leader lets it out in a kiai, the doors are blown in, and the axemen rush into the city. Shouts can be used to sharpen blades or to strike enemies. A common effect is the shout that knocks an enemy back, or the power of command. A strong Nord can instill bravery in men with his battle-cry, or stop a charging warrior with a roar. The greatest of the Nords can call to specific people over hundreds of miles, and can move by casting a shout, appearing where it lands." - The Elder Scrolls Wiki

Does this mean all Nords can use shouts?

I believe so, they just need training.

With the exception of someone who is Dragonborn, is Shouting an ability that is strictly limited to Nords, or is it that only Nords ever really receive training in using the Voice due to High Hrothgar being in Skyrim?

More or less. It's a heavy undertaking though, and takes years to even articulate a single shout however. But yes, every Nord has the capacity to learn how to use the Thu'um, thanks in part to Kyne.

EDIT: Nords are historically associated with shouting, as it was a large part of their own culture. If the Akaviri kiai is similar in function, the other races might be able to do it as well, but it took a divine intervention on Kynes part to make it happen. The other races usually have their own cracked out power, so its usefulness is negligible there.

Do races other than Nords have the ability to learn shouts? I always assumed so. And if so do we have any idea on whether only a few can learn shouts or whether everybody can shout, they just need to be taught.

EDIT: Whoops. Ninja'd.

Guess this would be interesting to study in the case of half or quarter Nords to see how much Nord ancestry it takes to have the capacity to Shout. Because if it is a one drop rule, a huge portion of the population would most likely have at least the capacity to Shout, even if they don't have the training to do so.

Who said it was hereditary to begin with? Seemed like anyone that was willing and able could be taught to shout back in the good ol' days. The Greybeards now are incredibly insular as it stands, and will only accept anyone they feel is able to become one of them. Even then, its a shot in the dark when you look at guys like Ulfric.

EDIT: Misread the comment entirely. Probably Nord enough to make it to Sovngard, at the very least.

On a completely side note but figured I'd bring it up now since I dont' want a separate thread, is the Spirit Blade of the Redguards another type of racial ability, such as Shouting. Also, what exactly is the racial difference between Cyrollics and Nords, in that the latter can use the Voice but Im not sure of any non-Dragonborn Cyrollics that were able to?