There seems to be a lot of history about the types of swords used and their development throughout history, but not really the extent of their use. And most modern sword use is largely for sport or ceremonial. Do we just romanticize swords because they're "really cool" and single combat with swords is so cinematic, or was there a time when everyone was literally carrying a sword of some sort on their hip?
The most common weapons were spears and their variants.
Since a medieval spear required only a small amount of steel along the sharpened edges (most of the spear-tip was wrought iron), it was an economical weapon. Quick to manufacture, and needing less smithing skill than a sword, it remained the main weapon of the common soldier
http://en.wikipedia.org/wiki/Spear#European_Middle_Ages
It was used in virtually every conflict up until the modern era and is probably the most commonly used weapon in history.
It's important to remember that swords are expensive, upper-class weapons in many societies. They are a mark of staus in cultures that have a kind of "cult of the sword.
From c. 1490-1750 every European male with any pretension to being a gentleman walked around with his sword on his hip. So did any Tokugawa samurai to proclaim his status.
Swords were inefficient? Compared to what? A gun? Certainly. Against what? Plate armour? Yes. But that horses are now largely for sport or ceremonial today and nowhere near as efficient as ATVs doesn't mean they weren't greatly used and desired in earlier eras.
Think of it this way. People going in harm's way try to carry the best weapons they can afford or are allowed. If the warriors with the most money are buying and training with swords, not just for a generation or a century but thousands of years, swords are probably pretty efficient at what they do. I do not comprehend why you think they aren't based on a very thin background.
What swords do well is close-in combat, not nose-to-nose like a knife, but not off at the range of lances.
The ancient world lacked a cult of the sword, as the knight and samurai had, and relied on phalanxes of spearmen, both the hoplite and the legionnaire. Both of them were considered ill-equipped without a sword! If swords were inefficient or too expensive for their worth, they would not have bothered carrying them. (Warry, Warfare in the Classical World) Long weapons always need to be backed up for when enemies press in under the range of the spear, and if they have swords and you don't, you lose.
Also evidential of the sheer usefulness of the sword is its use by mediaeval merchants on the road. (Ohler, The Medieval Traveller) Knights could wear ther swords on their belts or a baldric. Those of the lower class could not own one, by law. A merchant, travelling where there might be bandits, can have any weapon he likes to defend his life. What does he choose? A sword, carried on his saddle, or in his hand, but not worn, which would be illegal. It does not makehim pass as a noble. But it's efficient at keeping him alive. If a lance were better, he'd carry it instead.
Well, certainly not everyone. One needs to take into account that a sword was (is) an expensive weapon. You need a skilled smith and good metal. It's much easier and cheaper to hammer out an axehead or a spearpoint. It is mainly for this reason that swords tend to be the 'signature weapon' for higher classes in many cultures and civilizations.