Nap :
Well, not to be too picky, but that statement is very broad. If you want to be general then yes, I agree that a sword is in general my personal pick the best melee weapon. It is, after all, a sharp edge designed to be swung and cut something that doesn't operate well in two pieces (i.e. a body).
However, the type of weapon would depend upon the circumstances.
A cutting sword, like the Katana, would be my first choice against lightly armored foes (e.g. Samurai in bamboo armor). Against a steel-armored knight, the katana is more likely to bounce or slide off, rather then cut through, so I would change my preference to a piercing weapon like a falx (yes, it's a sword), heavy broadsword, axe or a mace that would crush my opponent to strawberry jam pre-packaged in its own tin. The Roman short sword is designed for stabbing in close quarters and very effective when combined with a large shield, and a lot of others legionaires in close formation.
As I said earlier, every weapon has its advantages and disadvantages. If it had no advantages, it wouldn't be used. Often that advantage was simply that it could be made cheaply and easily, or was available to peasants, whereas a sword was a custom-built fighting weapon with one purpose only. Still, in a one-on-one fight it really comes down to who is the master of their particular weapon. I'm sure there are skilled masters of the staff, spear etc. who could defeat most swordsmen, and vice versa.