There is a world of different swords, so don't just say generic "sword."
Each type of swords are used in a different way.
Curved swords are less effective against armor, tending to glance off them, rather then penetrate a weak spot.
There is a world of weapons out there, amazing and awesome looking ones, ones that look impressive, but probably didn't work well.
Swords, pikes, axes, combonation of the two, weapons made to unseat a mounted rider(many axes could do this), weapons that could be used by lower class, such as work implements that were lethal in the persons unique trained hands.
I do think to many "fantasy" writers limit themselves to the "sword".
As others have said, the weapon has to fit the person. IF they come from a metal poor area, they will use more wooden weapons with small metal pieces or even no metal at all. (staff and bow and arrow(flint arrow heads)
Poor social areas might be more likely to use every day objects as a weapon, with or without modifications. Even more so if the government restricted "weapons" to certain people or only government agents(military, police, Sheriff, nobles, bodyguards of such) Remember, Government control of weapons wasn't first thought of with firearms.
I think the problem is most "fantasy" writers stick with the classic European style fantasy and ignore any of the other cultures that existed during that time period. Swords are a popular image from the Middle Ages. However, even among England, you can see a wide variety of weapons in use. The fabled longbow, staves, spears, polearms, knives, etc were common among the infantry as most of them were the working class who used bows to hunt and staff type implements on a daily basis to survive.
If you look at other cultures and time periods, you can get a lot more interesting weapons. Asian cultures have great examples of using farming implements as weapons. The sais come from a farming tool used for planting rice patties. The kama was used for reaping grains. These implements-turned-weapons were used because the farmers had to turn into fighters to defend their homes.
Another side of weapons people forget about its culture doesn't just inform weaponry. Weaponry also informs culture. The taiko drums popular from the Japanese culture originally came from Korea. The Koreans developed these drums as a way of teaching how to fight with tahn bong (short sticks). This came about due to the Japanese outlawing martial arts in Korea while they occupied it to prevent an uprising.