Cracked.com this week has thrown up an article entitled: The 5 Weapon Myths you Probably Believe Thanks to the Movies. Myth #4 is that the sword's edge was used to parry incoming blows.
In the most masterful of internet-based research, the writer has cited a misguided article by John Clements and two – as far as I can tell randomy selected – videos of reenactment fighting as a firm counter to this "myth". The statement is that parries are almost never displayed in historical fencing manuals – which he says favour dodging and talking about pantaloons – and that when parrying is done it is done with the flat, not the edge.
Now I'm not an expert on Japanese swordplay (the article cites a fight in kill bill done with katanas as inaccurate) but I can certainly state that the edge-parry plays a fundamental role in pretty much all medieval and renaissance European fighting systems. Now I will agree that an optimal parry is generally not a 90-degree meeting of edges, this leads you into a full meeting of your opponent's force, which often you don't want. Meeting with your edge at an indirect angle to the path of force of the opponent is generally more ideal however not always possible. A bulk of techniques from manuals are derived from edge on edge interactions, many come when two attacks meet or when the defence is made from an attack into the attacking weapon and both combatants turning their edges toward one another to "bind". The idea that parrying plays a minor role in fencing manuals of the period or that the predominant method of parrying is done with the flat is completely unfounded both based on the written and pictorial examples found in historical manuals, which clearly direct edge parries and plenty of parries in general, and based on the physical properties of the weapon and biomechanical properties of the body.
Now I could beat this dead horse myself (this argument has flared up a few times in historical fencing circles) but instead I will direct all of you to a very fine, and well researched article, by Andrea Morini on the Hroarr.com website. This article is definitely worth a read and will save you from the myth of this myth.